Research ArticleContinuous Probabilistic Skyline Queries for Uncertain MovingObjects in Road Network

Shanliang Pan Yihong Dong Jinfeng Cao and Ken Chen

College of Information Science and Engineering Ningbo University Ningbo 315211 China

Correspondence should be addressed to Yihong Dong dongyihongnbueducn

Received 24 November 2013 Accepted 5 January 2014 Published 4 March 2014

Academic Editor Zhongwen Guo

Copyright copy 2014 Shanliang Pan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Inmoving environment the positions of moving objects cannot be located accurately Apart from themeasuring instrument errorsmovement of the objects is the main factor contributing to this uncertainty This uncertainty makes dominant relationship of datainstable which will affect skyline operator In this paper we mainly study the continuous probabilistic skyline query for uncertainmoving objects in road network The query point is deemed to be stationary while moving objects are treated as targets withuncertainty described by a probability density function After defining the notion of dominant probability and probabilistic skylinewe put forward a novel algorithm to deal with continuous probabilistic skyline query on road network Firstly we compute thedominant probability and skyline probability to get initial permanent p-skyline setThen we define events to predict the time whendominant relationship between moving objects may change Furthermore we track and calculate events to update the probabilisticskyline in an incremental way Two pruning strategies are proposed to cancel invalid events and objects in a bid to diminish searchspace Finally an extensive experimental evaluation on real datasets shows that probabilistic skyline sets in road network can beupdated by the proposed algorithm It demonstrates both efficiency and effectiveness

1 Introduction

Skyline query aims to find a subset where all objects are notdominated by any other object in the dataset helping usersinmulticriteria decisionmaking datamining and visualizingfor database and so forth

In mobile database a moving object reports its positionand velocity to database service through wireless communi-cation interface Because of time delay and other technicallimitations the position obtained usually deviates fromactualone The deviation causes what is called uncertainty whichleads to instability of dominant relationship between objectsIn real world objects are restricted in road network suchas track road or highway Position uncertainty of movingobjects including its environment should be considered inskyline operation

Until recently a lot of work on skyline query had beenfocused on a static dataset where the distances from querypoint to target objects are invariant With rapid developmentof GPS technology and mobile devices the location-basedservice (LBS) [1] which is pervasive in daily life is becoming

one of the most important applications in spatiotemporaldatabase However in moving environment moving objectswhose position is detected by GPS system alternately arealways in motion Delay or error of the sensor in GPSespecially the self-motion of moving objects makes thelocation of moving objects uncertain Despite the existinguncertainty the position is often treated as being accurate tobe queried inmany studies [2 3] Study on continuous skylinequery on moving objects was first proposed by Huang et al[4] In his work position of moving objects is considered asthe data with certainty

In fact because of the sensorsrsquo error and the objectsrsquomovement the position of objects in moving environment isuncertain and vague Recently a few researchers have beenaware of this imprecision and made some contributions [5ndash7] In our approach the location of query object is exactlyknown as a stationary object but the location of movingtarget objects is characterized by a certain distribution insteadof a precise point For example a weapon-related crime takesplace somewhere which is located in point 119874 as Figure 1shows Police cars should be dispatched to intervene The

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2014 Article ID 365064 13 pageshttpdxdoiorg1011552014365064

2 International Journal of Distributed Sensor Networks

adequate police strength including the number of policemenand equipment in the dispatched car is needed Also a caras near to the crime scene as possible is another factor forconsideration in order to arrive in time In Figure 1 tableshows the parameters of each police car including position ofthe cars number of policeman equipment level and networkdistance to the query point 119874 where the value of equipmentlevel is used to quantify the level of equipment with greatervalue corresponding to higher level If the police cars aretreated as certain points cars 119860 and 119864 are skyline objectsHowever the cars are moving quickly so their positions areuncertain to some extent For example suppose that the trueposition of car 119860 is at point 1198601015840 where the distance from 1198601015840to 119874 is 130 instead of 125 and car 119861rsquos actual position is atpoint 1198611015840 whose distance to 119874 is 125 In this case car 119861 candominate car 119860 so car 119860 is not skyline object Because ofroad network limitation the uncertain area is represented asa line centered on its acquired location as Figure 1 shows Inorder to simplify this scene probability density function 119891(119905)assumes uniform distribution and the police car 119861 is possibleto be skyline object

In this paper we address the problem of continuousprobabilistic skyline query for uncertain moving objects inroad network In our study case the query object stays stillwhile the target objects are moving with uncertainty whichis characterized by both a closed uncertainty region and aprobability density function (pdf) The main contributionsare as follows

(1) Probabilistic skyline on uncertain moving object inroad network is introduced as a new important issuein decision support or navigation systems

(2) By analyzing the dominant relationship betweenmoving objects in uncertain position environmentthe dominant probability and skyline probability aredefined in case the query is stationary with targetsmoving

(3) Based on trigger events which are presented to trackthe change of dominant relationship a novel algo-rithm Probabilistic Skyline query with Uncertaintyin Road network (PSUR) is proposed to deal withthe dynamic skyline query with uncertainty A seriesof pruning strategies are introduced to optimize andfasten this incremental algorithm

(4) A great deal of experiments on two truth datasets areconducted to analyze the uncertain region numbersof static dimensions velocity of moving objectsand dataset size that affect the algorithm Contrastexperiments from literature [8] are made to validatethe proposed PSUR The experimental results showthat PSUR is effective and efficient

The rest of this paper is organized as follows In Section 2we summarize the related work of skyline computationIn Section 3 after describing basic notion of skyline anduncertain model for moving objects we define dominantprobability and probabilistic skyline Section 4 introducestrigger events to track how dominant probability relationship

E O

A

B

D

C

50

30

30

30

60

6060

40

10

50

A998400

B998400

Figure 1 An example of skyline query for uncertain data

varies when objects are moving with uncertainty Two prun-ing strategies are adopted to reduce the search space Section 5describes PSUR algorithm to update 119901-skyline set Section 6gives experimental evaluation on two real datasets Finallythe conclusion is reached in Section 7

2 Related Work

Skyline queries are hot areas of current database researchwhich recently have attracted more and more attention It isintroduced into relational database firstly by Borzsony et al[9] with two proposed processing algorithms Block-Nested-loops algorithm (BNL) and Extended Divide amp Conqueralgorithm (DampC) As an improved method of BNL proposedbyDrChomicki et al Sort-Filter-Skyline algorithm (SFS) [10]constructs the multidecision dominative order chains for theordered dataNNalgorithm [11] based onR-tree searches thenearest neighbor recursively It speeds up the skyline queryby reducing the comparison numbers of BNL among objectsNevertheless it will cost more time and space in searchingsubspace repeatedly Overcoming this limitation the sortedR-tree based BBS [12] is proposed It is one of the best skylinequery methods in centralized datasets

In recent years skyline query has been extended tothe dynamic datasets The R-tree based I-Eager and I-Lazyalgorithms were brought forth by Tao and Papadias [13] whofirstly studied how to update and maintain the skyline resultsin dynamic datasets Tian et al [14] introduced GICSCupdating skyline query sets dynamically which better fits forlow dimension metrics Kontaki et al [15] exerted efforts tomaintain 119896-dominant skyline objects with maximum userrsquospreference Huang et al [4] probed into the continuousskyline query for certain moving objects It assumes that allpoints including the query point move in a predictable wayAfter analyzing dominating relationship between points inthe space Huang presented a continuous tracking algorithm-CSQ to maintain skyline sets dynamically

In sensor networks andmoving environment the charac-ters of the objects are not exactly known due to the limitationsof measuring equipment and objectsrsquo movement A lot ofwork has focused on uncertain data The authors in [5] stud-ied the execution of probabilistic range and nearest-neighbor

International Journal of Distributed Sensor Networks 3

queries in mobile environment The author in [16] focusedon the situation in which the location of a query object is notexactly known In research of skyline query field Fiedler [17]firstly proposed skyline operator on uncertain data in his dis-sertation Pei et al [18] proposed a probabilistic skylinemodelformultiinstance data where each object is part of the skylinewith a certain probability They presented two algorithmsBUM and TDM to study skyline query on uncertain data ofthe possible worldmodel (PWM) Lian andChen [19] studiedreverse-skyline queryTheymodeled the probabilistic reverseskyline query on uncertain data in both monochromaticand bichromatic case and proposed two effective pruningmethods MPRS and BPRS to reduce the search space ofquery processing Zhang et al [20] explored how to maintainskyline sets when uncertain data are updated An AR-tree isconstructed for all uncertain data and the maintenance isinserting deleting and updating on this AR-treeThe authorsin [21] designed partitioning method to compute skylineprobabilities for discrete data with uncertainty The authorsin [8] investigated skyline probabilities with a parametricform pdf (eg a Gaussian function or a Gaussian mixturemodel) The authors in [22] proposed a sliding windowskyline model to study the execution of the probabilisticskyline query over uncertain data streams [23] The authorsstudied a new problem of range-based skyline queries Twonovel algorithms I-SKY and N-SKY were presented to solvethe probabilistic and continuous range-based skyline queries

In road network Huang and Jensen [24] assumed thatthe userrsquos movement is constrained to a road network Theauthors defined route nearest-neighbour skyline queries toconsider the computation efficiency Deng et al [25] studiedmultisource skyline query in road networks Three differentroad networks ofmultisource querymethods were presentedThe authors in [26] proposed a new method to processcontinuous skyline in road network based on precomputingthe shortest range data of targets The authors in [27]introduced route skyline computation in a multiattributegraph Top routes are computed iteratively in an efficient wayand pruning technique is adopted in order to reduce thesearch space The authors in [28] focused on extracting thepath skylines and proposed PathSL to generate an optimalskyline for moving objects

In spite of much work focusing on uncertainty of skylinequeries or route skyline queries there is little work completedfor skyline query concerning uncertainty of moving objectsThe authors in [4 22ndash25] ignored the uncertainty of movingobjects while the authors [8 18 21] dealt with discrete datawith independent dominant relationship between objects Itis the first time to compute continuous probabilistic skylinequery with regard to uncertainty of moving objects in roadnetwork

3 The Probabilistic Skyline for UncertainMoving Objects

31 Skyline on Certain Points Suppose that the point setis 119878 = 119904

1 1199042 119904Num where Num is the number

of points each point in an 119899-dimensional numeric space

Table 1

Position of police car A B C D ENumber of policemen 6 6 6 4 5Equipment level 3 3 2 3 2Network distance to 119874 125 130 140 155 90

119863 = 1198891 1198892 119889

119899 The original concept of skyline is based

on the notion of dominance Let 119883 = (1199091 1199092 119909

119899) 119884 =

(1199101 1199102 119910

119899) 119883 isin 119878 119884 isin 119878 if forall119894 119909

119894le 119910119894(1 le 119894 le 119899) and

exist119895 satisfy 119909119895lt 119910119895(1 le 119895 le 119899) then 119883 is said to dominate

119884 donated by 119883 ≺ 119884 Given a set of objects 119878 an object 119883 isa skyline point if there is not any other point dominating 119883The skyline on 119878 is the set of all skyline points

32 Uncertain Model for Moving Objects After Wolfsonet al [1] firstly studied the uncertainty of moving objectsa lot of work has focused on this field [5ndash7] An uncertainregion [5] of a moving object119872119894 at time 119905 denoted by 119880119894(119905)is a closed irregular region with a velocity V such that therecorded location 119874

119894can be found only inside this region

The pdf represents the probability density distribution of anobject in its uncertain region The uncertainty pdf [5] of anobject119872119894 denoted by 119891(119900

119894) is a pdf of 119874

119894 that has a value of

0 outside 119880119894(119905)

33TheDominant Probability Whatwemainly study on is asfollows There is a set of moving target objects whose centersare 119874 = 119900

1 1199002 119900Num isin 119877

119899 and a stationary object 119902 asa query point to continuously compute updated probabilisticskyline dataset

Dissimilar to the traditional skyline query in movingenvironment the spatial location is changing with time Allattributes are divided into dynamic attributes and static onesLet us suppose that there are 119898 dynamic attributes 119896 staticattributes and 119899 attributes where 119899 = 119898 + 119896 For each object119874119894= (119909119894

1 119909119894

2 119909

119894

119889)119879 the static attributes construct a vector

denoted by119874119878119894= (119909119894

1198781 119909119894

1198782 119909

119894

119878119896)119879 while the dynamic ones

are made up of a vector 119874119889119894= (119909119894

1198891 119909119894

1198892 119909

119894

119889119898)119879 where

119899 = 119896+119898 For instance in Figure 1 the number of police andequipment level belong to static attributes because they areinvariant in our study case However the distance from119874

119894to

119902 is varying continuously with police car119874119894moving In order

to simplify the description dynamic attributes are supposedto include only spatial position (Table 1)

Definition 1 (dominant probability) Let 119874119894 119874119895be two mov-

ing objects with uncertainty and 119902 be a stationary query pointThen probability that 119874

119895dominates 119874

119894is

119901 (119900119895≺ 119900119894)

= int119880119903119874119895

int119880119903119874119894

119891119874119894( 119909119894) 119891119874119895( 119909119895) isdom ( 119909

119895 119909119894) 119889119900119894119889119900119895

(1)

where 119891119874119894( 119909119894) and 119891

119874119895( 119909119895) are probability density function of

object 119874119894and 119874

119895 119909119895isin 119880119903(119874

119895) 119909119894isin 119880119903(119874

119894) and function

4 International Journal of Distributed Sensor Networks

q

Oj

xj

xi

Ur(Oj)

Oi

Ur(Oi)

Figure 2 Dominant probability

isdom ( 119909119895 119909119894) =

1 dist( 119909119895 119902)ledist( 119909119894 119902)0 otherwise dist( 119909

119895 119902) is

Euclidean distance between 119909119895and 119902

According to the definition of dominance in (1) wemaintain that 119874

119895can have dominance probability on 119874

119894only

if the static attributes of 119874119895dominate the static ones of 119874

119894

As shown in Figure 2 for arbitrary point 119909119895in 119880119903(119874

119895) each

point 119909119894in119880119903(119874

119894) that satisfies dist( 119909

119895 119902) le dist( 119909

119894 119902)will be

dominated by 119909119895 as the hatched area shows

34 The Skyline Probability

Definition 2 (skyline probability) The skyline probability ofobject 119874

119894is the likelihood that object 119874

119894is not dominated by

any other object and is defined below

Pr (119900119894) = Pr( and

119874119895isin119874

119874119895 ≺ 119874119894)

= int119880119903119874119894

119891119874119894( 119909119894)

timesprod(1 minus int119891119874119895( 119909119895) isdom ( 119909

119894 119909119895) 119889119900119895)119889119900119894

(2)

where 119891119874119894( 119909119894) and 119891

119874119895( 119909119895) are probability density function of

object 119874119894and 119874

119895 respectively 119909

119895isin 119880119903(119874

119895) 119909119894isin 119880119903(119874

119894)

Definition 3 (119901-skyline) Let 119901 isin [0 sdot sdot sdot 1] be a threshold The119901-skyline is the set of objects for which the following propertyholds

119878120591= 119874119894isin 119874 | Pr (119874

119894) ge 119901 (3)

35 UncertainModel in RoadNetwork The road network canbe treated as a nondirection graph 119866 = ⟨119881 119864119882⟩ where 119881 isnode set representing crossroad 119864 is edge representing roadsbetween two crossroads and119882 is length of 119864

r Coi

UI(t)

A(t)

Figure 3 Uncertain model in road network

In road network the objects are limited movement sothe uncertain domain is denoted by a line segment with 119891(119905)distribution which 119891(119905) is pdf as Figure 3 shows

Denote 119889(V V1015840) by the shortest path between nodes V andV1015840 119889(V V1015840) = infin if there exists no path from V to V1015840 In roadnetwork the distance is represented by shortest path

Definition 4 (minimum distance function) The minimumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889min(119902 119900119894) = 119889(119902 119900119894) minus 119903

Definition 5 (maximum distance function) The maximumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889max(119902 119900119894) = 119889(119902 119900119894) + 119903

In continuous movement the dominant relationship oftwo objects will change For two moving objects 119874

119894and 119874

119895

119901 (119900119895≺ 119900119894)

=

1

119889max (119902 119900119895) le 119889min (119902 119900119894)

0

119889min (119902 119900119895) ge 119889max (119902 119900119894)

int119880119903119874119895

int119880119903119874119894

119891119874119894( 119909119894) 119891119874119895( 119909119895) isdom ( 119909

119895 119909119894) 119889119900119894119889119900119895

119889min (119902 119900119895) lt 119889max (119902 119900119894)

119889max (119902 119900119895) gt 119889min (119902 119900119894)

(4)

The maximum and minimum distance functions maybeintersect with each other among moving objects Two dis-tance functions of object119874

119894and119874

119895are given in Figure 4The

maximum distance of 119874119894is less than the minimum distance

of 119874119895prior to time 119905

1 so 119874

119895cannot dominate 119874

119894 119874119895might

begin to dominate119874119894from 119905

1to 1199052 as the hatched area shows

so does it from 1199053to 1199054 and from 119905

5to 1199056

4 Tracking by Events

Theprobabilistic skyline set is updated in an incremental wayThe key step is how to predict the time when the dominantrelationship changes Itrsquos hard to know the accurate timewhen119901-skyline just change But we can estimate period of timeduring which the 119901-skyline may change

41 Trigger Events As shown in Figure 4 from time 1199051to

time 1199052 the dominant relationship between 119874

119894and 119874

119895might

change because the maximum distance of 119874119894is greater than

the minimum distance of 119874119895 So we call the time between

International Journal of Distributed Sensor Networks 5

Oj

d

tqt1 t2 t3 t4 t5 t6

d (q oj)d (q oi )

d (q oi)d (q oj)

Oi

Figure 4 Transformation of dominant relationship

1199051and 119905

2an event An event on 119874

119894can be presented as

119890V119890119899119905(119900119894 119900119895) = ⟨119900

119894 119900119895 119904 119905119894119898119890 119890 119905119894119898119890⟩ where 119874

119894and 119874

119895are

two objects whose dominant relationshipmay be variedwhen119904 119905119894119898119890 and 119890 119905119894119898119890 are start time and end time of the eventrespectively

42 The Pruning Strategy for Events By analyzingrelationship of objects we know that if static charactersof any two objects 119874

119894and 119874

119895have dominant relationship

supposing that 119874119878119895≺ 119874119878

119894 an event maybe occur With the

query object moving a considerable amount of events willoccur In order to improve effectiveness of our algorithm wepropose a series of event pruning strategies

Pruning Strategy 1 If the dominant relationship in staticattributes between two moving objects 119874

119894and 119874

119895does

not exist the intersection of those two distance functionswill cause no variation to 119901-skyline set In this case theintersection will not cause any event

Proof Suppose 119900119894= (119909119894

1 119909119894

2 119909

119894

119889) 119900119895= (119909119895

1 119909119895

2 119909

119895

119889)

whose static characters are 119900119878

119894= (119909119894

1199041 119909119894

1199042 119909

119894

119904119896) and

119900119878

119895=

(119909119895

1199041 119909119895

1199042 119909

119895

119904119896) respectively It is known that the static char-

acters of119874119894and119874

119895do not possess any dominant relationship

so exist119896119901 119896119902 119909119894

119896119901gt 119909119895

119896119901

and 119909119894119896119902lt 119909119895

119896119902

Even consideringtheir dynamic attributes the dominant relationship does notexist at any time In conclusion if the dominant relationshipin static attributes between two objects does not exist theintersection of their distance functions will not cause anychange for their dominant probability Events cannot takeplace

Pruning Strategy 2 Suppose exist119900119894 119900119895 119901(119900119895≺ 119900119894) = 1

Event(119894 119895 119905begin 119905end) is an event interrelated to 119874119894and 119874

119895

If existevent(119874119894 119874119896 1199051015840

begin 1199051015840

end) (0 lt 119896 lt Num and 119896 = 119894)

and 1199051015840begin lt 119905begin the computation for event(119874119894 119874119896

1199051015840

begin 1199051015840

end) is invalid before 119905begin However if 1199051015840

end lt 119905beginevent(119894 119896 1199051015840begin 119905

1015840

end) is also invalid

Proof Because 119901(119900119895≺ 119900119894) = 1 it is known that 119901(119900

119894≺ 119900119895) = 0

prior to time 119905begin The update for event(119874119894 119874119896 1199051015840

begin 1199051015840

end) isinvalid It is also invalid when 1199051015840end lt 119905begin

5 Continuous Probabilistic SkylineQueries Algorithm

51 Initialization The initialization framework is presentedin this section Each object has static and dynamic attributesso we should compute the dominance relation on staticattributes firstly For two objects 119874

119894and 119874

119895 119874119895might

dominate 119874119894only when 119900119878

119895≺ 119900119878

119894(Algorithm 1) In order to

compute fast static skyline set denoted by 119878static is introducedif only the dominant relationship for static characters isconsidered

In any case objects move 119878static always belongs to skylineIn initialization step the moving path and distance functionof each moving object need to be precomputed according tothe information of road network and moving objects apartfrom 119878static

52 PSUR Algorithm Not all skyline probability of objectswill change at one moment If maximumminimum distancefunction of one object cuts that of others in Cartesiancoordinates skyline probability of this object maybe vary(Algorithm 2) In other words trigger events include allpossible variations of 119901-skyline for each moving object

In order to simplify the problem we suppose that allmoving objects preserve their velocity with uniform speedIf not the precomputing cannot be processed in advanceAll events should be recomputed again The movement ofmoving objects to query point can be picked up with itsshortest path to query point The intersecting time for thedistance function can be recomputed and put into eventqueue sorted by time in ascending order For each timeskyline probabilities of moving objects under trigger eventsneed to be updated

53 Algorithm Analysis and Discussion The cost incurredby our method consists of three components initializationevents computing and updating by tracking

In initialization period computing static dominant rela-tionship will cost 119874(119889 sdot 119899(119899 minus 1)2) where 119889 is staticdimensional degreeThemost cost is skyline probability com-putation The famous Simpson integration method which isintroduced to compute skyline probability of each movingobjects Num and time interval 119905 Probabilistic 119874((Lenℎ)2)where Len is uncertain segment length and ℎ is step widthof Simpson so the cost of skyline probability of each movingobject is119874((Lenℎ)2(119899minus1)) After skyline probability compu-tation judgment for 119901-skyline objects will cost 119874(119899) Above

6 International Journal of Distributed Sensor Networks

Input one query object 119899moving objectsOutput Initialization 119901-skyline(1) 119878static = NULL(2) for any point 119900

119894in 119874

(3) compute path(119900119894) get the moving path of objects

(4) compute distance(119900119894) computing distance function

(5) 119874119894= NULL

(6) for any point 119900119895(119895 = 119894) in 119874

(7) compare(119900119878119895 119900119878119894) ensure whether 119874

119895dominate 119874

119894in static attributes

(8) if 119900119878119895≺ 119900119878

119894

(9) flag(119900119895 119900119894) = 1

(10) push 119900119895into the 119874

119894

(11) else(12) flag(119900

119895 119900119894) = 0

(13) if the 119874119894= NULL

(14) 119878static = 119878static cup 119900119894

Algorithm 1 Initialization

Input the set of moving objects119863 query point 119902 119901 is the probabilistic threshold the time interval [119905119904 119905119890]

Output the 119901-Skyline at any time instant 119905 within [119905119904 119905119890]

(1) initialization()(2) compute events(3) for any point 119900

119894in 119874

(4) for each point 119900119895in 119874119894

(5) compute begin time s time and end time e time of each event(6) if s time le 119905

119890ampamp e time ge 119905

119904

(7) push it into 119876119890 valid event

(8) handle events(9) time = 119905

119904 119871119901= 119871119904

(10) while (time le 119905119890)

(11) while (119876119890= NULL)

(12) 119890 = 119876119890sdot erase() pop queuersquos head

(13) while (119890 sdot 119905begin le time)(14) 119876handle sdot push back(119890) push 119890 into queue(15) 119890 = 119876

119890sdot erase()

(16) handle(119876handle) update 119876119890 and 119878119901(17) time++

Algorithm 2 PSUR algorithm

all time cost in initialization is119874(119889sdot119899(119899minus1)2+(Lenℎ)2(119899minus1) + 119899)

In second step the worst cost of comparison for staticdominant relationship between objects is 119874(119899(119899 minus 1)2) Theinteraction time for arbitrary two moving objectsrsquo distancefunction will cost119874(120575

1) where 120575

1is constantThus it will cost

119874(1205751sdot 119899(119899 minus 1)2) in this period

Handling events generates at most 119899(119899 minus 1)2 In theworst case each event is valid in time period [119905

119904 119905119890] and

this requires (119905119890minus 119905119904) times to deal with events In every

processing skyline probability related to trigger events willcost 119874((Lenℎ)2(119899 minus 1)) while update computing for eventis 119874(120575

2) where 120575

2is constant The total cost in this period is

119874((Lenℎ)2(119899minus1)sdot(119905119890minus119905119904) sdot119899(119899minus1)2+120575

2sdot (119905119890minus119905119904) sdot119899(119899minus1)2)

In conclusion the total cost is added together for thesethree periods which is equivalent to 119874(1198992)

6 Experimental Evaluation

61 Datasets Two real road networks are used to test theeffect and efficiency of the proposed algorithm PSUR Oneis the famous seashore city Oldenburg in Germany whichincludes 6105 nodes and 7036 edges The other is Cixi city ofChina which contains 244 intersection nodes and 407 edgesmuch smaller than the first oneWe assume that the uncertainarea is segment along the road Two distributions of uniformand Gaussian distribution for probability density functionare adopted because these two functions are by far the mostimportant and commonly used in statistics Moving objectsare generated randomly Baseline and priority algorithmsproposed in [8] are used to compare with our method PSURto verify efficiency and effect The main parameters aresegment length Len static dimension number 119889 numbers of

International Journal of Distributed Sensor Networks 7

50 5000

2

4

6

8

10

12

14

N

times104

100 200 300 400

Runt

ime (

ms)

(a) Gaussian distribution

50 100 200 300 400 5000

2

4

6

8

10

12

Runt

ime (

ms)

PriorityBaseline

PSUR

N

times104

(b) Uniform distribution

Figure 5 Numbers of moving objects effects of the performance inCixi city (119889 = 5 Len = 10 and 119905 = 20)

moving objects Num and time interval 119905 and probabilisticthreshold 119901 is 05 in all experiments

We conducted our experiments on desktop PC runningon Windows XP professional The PC has Intel Core 2Duo293GHz and 3GB RAM memory All experiments werecoded in Visual C++ 2008

62 Numbers of Moving Objects In this experiment suppose119889 = 5 Len = 10 and 119905 = 20 Figure 5 shows performanceof PSUR versus baseline and priority [8] when numbersof moving objects vary on Cixirsquos road network both in

Table 2 Event size in Cixi road network (119889 = 5 Len = 10 119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 669 35

100 2721 95

200 10389 205

300 35009 400

400 62723 514

500 96890 736

Table 3 Event size in Oldenburg road network (119889 = 5 Len = 10119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 245 5

100 455 15

200 1557 41

300 3945 131

400 6464 236

500 9951 367

uniform distribution and Gaussian distribution LikewiseFigure 10 demonstrates the performance on road networkin Oldenburg The figures show that runtime increases withobjectrsquos numbers whichever the model is No matter whatmodel is used uniform or Gaussian the cost in the samedataset is similar Among these three methods the responsetime of our algorithm is only one-tenth of the other twomethods It is because baseline and priority need recomputethe probabilistic skyline set at each time while PSUR is anincremental method

If there is the same number of moving objects in tworeal networks the density of moving objects in Cixi isbigger than that in Oldenburg because Cixi is smaller thanOldenburg Therefore the chances for interaction of movingobjects in Cixi are more those that in Oldenburg Triggerevents generated in Cixi are evidently more than those inOldenburg as Tables 2 and 3 show The density of movingobjects leads to this difference because it is more sparselydistributed in Oldenburg than in Cixi for the same numberof objects As a result by observing the performance betweentwo city networks under the same data model such asFigures 5(a) and 6(a) it is noted that the runtime in thesmaller city Cixi costs a little more than that in Oldenburg

The pruning strategy has done effective work on eventsize as Tables 2 and 3 show Event size will grow withthe number of moving objects because the number of theintersection of distance function rises

63 The Effect of Uncertain Segment Length In this sectionparameters are as follows Num = 50 119889 = 5 and 119905 = 20Figures 7 and 8 show performance of three algorithms whensegment length of uncertainty varies on Cixi road network

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 International Journal of Distributed Sensor Networks

adequate police strength including the number of policemenand equipment in the dispatched car is needed Also a caras near to the crime scene as possible is another factor forconsideration in order to arrive in time In Figure 1 tableshows the parameters of each police car including position ofthe cars number of policeman equipment level and networkdistance to the query point 119874 where the value of equipmentlevel is used to quantify the level of equipment with greatervalue corresponding to higher level If the police cars aretreated as certain points cars 119860 and 119864 are skyline objectsHowever the cars are moving quickly so their positions areuncertain to some extent For example suppose that the trueposition of car 119860 is at point 1198601015840 where the distance from 1198601015840to 119874 is 130 instead of 125 and car 119861rsquos actual position is atpoint 1198611015840 whose distance to 119874 is 125 In this case car 119861 candominate car 119860 so car 119860 is not skyline object Because ofroad network limitation the uncertain area is represented asa line centered on its acquired location as Figure 1 shows Inorder to simplify this scene probability density function 119891(119905)assumes uniform distribution and the police car 119861 is possibleto be skyline object

In this paper we address the problem of continuousprobabilistic skyline query for uncertain moving objects inroad network In our study case the query object stays stillwhile the target objects are moving with uncertainty whichis characterized by both a closed uncertainty region and aprobability density function (pdf) The main contributionsare as follows

(1) Probabilistic skyline on uncertain moving object inroad network is introduced as a new important issuein decision support or navigation systems

(2) By analyzing the dominant relationship betweenmoving objects in uncertain position environmentthe dominant probability and skyline probability aredefined in case the query is stationary with targetsmoving

(3) Based on trigger events which are presented to trackthe change of dominant relationship a novel algo-rithm Probabilistic Skyline query with Uncertaintyin Road network (PSUR) is proposed to deal withthe dynamic skyline query with uncertainty A seriesof pruning strategies are introduced to optimize andfasten this incremental algorithm

(4) A great deal of experiments on two truth datasets areconducted to analyze the uncertain region numbersof static dimensions velocity of moving objectsand dataset size that affect the algorithm Contrastexperiments from literature [8] are made to validatethe proposed PSUR The experimental results showthat PSUR is effective and efficient

The rest of this paper is organized as follows In Section 2we summarize the related work of skyline computationIn Section 3 after describing basic notion of skyline anduncertain model for moving objects we define dominantprobability and probabilistic skyline Section 4 introducestrigger events to track how dominant probability relationship

E O

A

B

D

C

50

30

30

30

60

6060

40

10

50

A998400

B998400

Figure 1 An example of skyline query for uncertain data

varies when objects are moving with uncertainty Two prun-ing strategies are adopted to reduce the search space Section 5describes PSUR algorithm to update 119901-skyline set Section 6gives experimental evaluation on two real datasets Finallythe conclusion is reached in Section 7

2 Related Work

Skyline queries are hot areas of current database researchwhich recently have attracted more and more attention It isintroduced into relational database firstly by Borzsony et al[9] with two proposed processing algorithms Block-Nested-loops algorithm (BNL) and Extended Divide amp Conqueralgorithm (DampC) As an improved method of BNL proposedbyDrChomicki et al Sort-Filter-Skyline algorithm (SFS) [10]constructs the multidecision dominative order chains for theordered dataNNalgorithm [11] based onR-tree searches thenearest neighbor recursively It speeds up the skyline queryby reducing the comparison numbers of BNL among objectsNevertheless it will cost more time and space in searchingsubspace repeatedly Overcoming this limitation the sortedR-tree based BBS [12] is proposed It is one of the best skylinequery methods in centralized datasets

In recent years skyline query has been extended tothe dynamic datasets The R-tree based I-Eager and I-Lazyalgorithms were brought forth by Tao and Papadias [13] whofirstly studied how to update and maintain the skyline resultsin dynamic datasets Tian et al [14] introduced GICSCupdating skyline query sets dynamically which better fits forlow dimension metrics Kontaki et al [15] exerted efforts tomaintain 119896-dominant skyline objects with maximum userrsquospreference Huang et al [4] probed into the continuousskyline query for certain moving objects It assumes that allpoints including the query point move in a predictable wayAfter analyzing dominating relationship between points inthe space Huang presented a continuous tracking algorithm-CSQ to maintain skyline sets dynamically

In sensor networks andmoving environment the charac-ters of the objects are not exactly known due to the limitationsof measuring equipment and objectsrsquo movement A lot ofwork has focused on uncertain data The authors in [5] stud-ied the execution of probabilistic range and nearest-neighbor

International Journal of Distributed Sensor Networks 3

queries in mobile environment The author in [16] focusedon the situation in which the location of a query object is notexactly known In research of skyline query field Fiedler [17]firstly proposed skyline operator on uncertain data in his dis-sertation Pei et al [18] proposed a probabilistic skylinemodelformultiinstance data where each object is part of the skylinewith a certain probability They presented two algorithmsBUM and TDM to study skyline query on uncertain data ofthe possible worldmodel (PWM) Lian andChen [19] studiedreverse-skyline queryTheymodeled the probabilistic reverseskyline query on uncertain data in both monochromaticand bichromatic case and proposed two effective pruningmethods MPRS and BPRS to reduce the search space ofquery processing Zhang et al [20] explored how to maintainskyline sets when uncertain data are updated An AR-tree isconstructed for all uncertain data and the maintenance isinserting deleting and updating on this AR-treeThe authorsin [21] designed partitioning method to compute skylineprobabilities for discrete data with uncertainty The authorsin [8] investigated skyline probabilities with a parametricform pdf (eg a Gaussian function or a Gaussian mixturemodel) The authors in [22] proposed a sliding windowskyline model to study the execution of the probabilisticskyline query over uncertain data streams [23] The authorsstudied a new problem of range-based skyline queries Twonovel algorithms I-SKY and N-SKY were presented to solvethe probabilistic and continuous range-based skyline queries

In road network Huang and Jensen [24] assumed thatthe userrsquos movement is constrained to a road network Theauthors defined route nearest-neighbour skyline queries toconsider the computation efficiency Deng et al [25] studiedmultisource skyline query in road networks Three differentroad networks ofmultisource querymethods were presentedThe authors in [26] proposed a new method to processcontinuous skyline in road network based on precomputingthe shortest range data of targets The authors in [27]introduced route skyline computation in a multiattributegraph Top routes are computed iteratively in an efficient wayand pruning technique is adopted in order to reduce thesearch space The authors in [28] focused on extracting thepath skylines and proposed PathSL to generate an optimalskyline for moving objects

In spite of much work focusing on uncertainty of skylinequeries or route skyline queries there is little work completedfor skyline query concerning uncertainty of moving objectsThe authors in [4 22ndash25] ignored the uncertainty of movingobjects while the authors [8 18 21] dealt with discrete datawith independent dominant relationship between objects Itis the first time to compute continuous probabilistic skylinequery with regard to uncertainty of moving objects in roadnetwork

3 The Probabilistic Skyline for UncertainMoving Objects

31 Skyline on Certain Points Suppose that the point setis 119878 = 119904

1 1199042 119904Num where Num is the number

of points each point in an 119899-dimensional numeric space

Table 1

Position of police car A B C D ENumber of policemen 6 6 6 4 5Equipment level 3 3 2 3 2Network distance to 119874 125 130 140 155 90

119863 = 1198891 1198892 119889

119899 The original concept of skyline is based

on the notion of dominance Let 119883 = (1199091 1199092 119909

119899) 119884 =

(1199101 1199102 119910

119899) 119883 isin 119878 119884 isin 119878 if forall119894 119909

119894le 119910119894(1 le 119894 le 119899) and

exist119895 satisfy 119909119895lt 119910119895(1 le 119895 le 119899) then 119883 is said to dominate

119884 donated by 119883 ≺ 119884 Given a set of objects 119878 an object 119883 isa skyline point if there is not any other point dominating 119883The skyline on 119878 is the set of all skyline points

32 Uncertain Model for Moving Objects After Wolfsonet al [1] firstly studied the uncertainty of moving objectsa lot of work has focused on this field [5ndash7] An uncertainregion [5] of a moving object119872119894 at time 119905 denoted by 119880119894(119905)is a closed irregular region with a velocity V such that therecorded location 119874

119894can be found only inside this region

The pdf represents the probability density distribution of anobject in its uncertain region The uncertainty pdf [5] of anobject119872119894 denoted by 119891(119900

119894) is a pdf of 119874

119894 that has a value of

0 outside 119880119894(119905)

33TheDominant Probability Whatwemainly study on is asfollows There is a set of moving target objects whose centersare 119874 = 119900

1 1199002 119900Num isin 119877

119899 and a stationary object 119902 asa query point to continuously compute updated probabilisticskyline dataset

Dissimilar to the traditional skyline query in movingenvironment the spatial location is changing with time Allattributes are divided into dynamic attributes and static onesLet us suppose that there are 119898 dynamic attributes 119896 staticattributes and 119899 attributes where 119899 = 119898 + 119896 For each object119874119894= (119909119894

1 119909119894

2 119909

119894

119889)119879 the static attributes construct a vector

denoted by119874119878119894= (119909119894

1198781 119909119894

1198782 119909

119894

119878119896)119879 while the dynamic ones

are made up of a vector 119874119889119894= (119909119894

1198891 119909119894

1198892 119909

119894

119889119898)119879 where

119899 = 119896+119898 For instance in Figure 1 the number of police andequipment level belong to static attributes because they areinvariant in our study case However the distance from119874

119894to

119902 is varying continuously with police car119874119894moving In order

to simplify the description dynamic attributes are supposedto include only spatial position (Table 1)

Definition 1 (dominant probability) Let 119874119894 119874119895be two mov-

ing objects with uncertainty and 119902 be a stationary query pointThen probability that 119874

119895dominates 119874

119894is

119901 (119900119895≺ 119900119894)

= int119880119903119874119895

int119880119903119874119894

119891119874119894( 119909119894) 119891119874119895( 119909119895) isdom ( 119909

119895 119909119894) 119889119900119894119889119900119895

(1)

where 119891119874119894( 119909119894) and 119891

119874119895( 119909119895) are probability density function of

object 119874119894and 119874

119895 119909119895isin 119880119903(119874

119895) 119909119894isin 119880119903(119874

119894) and function

4 International Journal of Distributed Sensor Networks

q

Oj

xj

xi

Ur(Oj)

Oi

Ur(Oi)

Figure 2 Dominant probability

isdom ( 119909119895 119909119894) =

1 dist( 119909119895 119902)ledist( 119909119894 119902)0 otherwise dist( 119909

119895 119902) is

Euclidean distance between 119909119895and 119902

According to the definition of dominance in (1) wemaintain that 119874

119895can have dominance probability on 119874

119894only

if the static attributes of 119874119895dominate the static ones of 119874

119894

As shown in Figure 2 for arbitrary point 119909119895in 119880119903(119874

119895) each

point 119909119894in119880119903(119874

119894) that satisfies dist( 119909

119895 119902) le dist( 119909

119894 119902)will be

dominated by 119909119895 as the hatched area shows

34 The Skyline Probability

Definition 2 (skyline probability) The skyline probability ofobject 119874

119894is the likelihood that object 119874

119894is not dominated by

any other object and is defined below

Pr (119900119894) = Pr( and

119874119895isin119874

119874119895 ≺ 119874119894)

= int119880119903119874119894

119891119874119894( 119909119894)

timesprod(1 minus int119891119874119895( 119909119895) isdom ( 119909

119894 119909119895) 119889119900119895)119889119900119894

(2)

where 119891119874119894( 119909119894) and 119891

119874119895( 119909119895) are probability density function of

object 119874119894and 119874

119895 respectively 119909

119895isin 119880119903(119874

119895) 119909119894isin 119880119903(119874

119894)

Definition 3 (119901-skyline) Let 119901 isin [0 sdot sdot sdot 1] be a threshold The119901-skyline is the set of objects for which the following propertyholds

119878120591= 119874119894isin 119874 | Pr (119874

119894) ge 119901 (3)

35 UncertainModel in RoadNetwork The road network canbe treated as a nondirection graph 119866 = ⟨119881 119864119882⟩ where 119881 isnode set representing crossroad 119864 is edge representing roadsbetween two crossroads and119882 is length of 119864

r Coi

UI(t)

A(t)

Figure 3 Uncertain model in road network

In road network the objects are limited movement sothe uncertain domain is denoted by a line segment with 119891(119905)distribution which 119891(119905) is pdf as Figure 3 shows

Denote 119889(V V1015840) by the shortest path between nodes V andV1015840 119889(V V1015840) = infin if there exists no path from V to V1015840 In roadnetwork the distance is represented by shortest path

Definition 4 (minimum distance function) The minimumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889min(119902 119900119894) = 119889(119902 119900119894) minus 119903

Definition 5 (maximum distance function) The maximumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889max(119902 119900119894) = 119889(119902 119900119894) + 119903

In continuous movement the dominant relationship oftwo objects will change For two moving objects 119874

119894and 119874

119895

119901 (119900119895≺ 119900119894)

=

1

119889max (119902 119900119895) le 119889min (119902 119900119894)

0

119889min (119902 119900119895) ge 119889max (119902 119900119894)

int119880119903119874119895

int119880119903119874119894

119891119874119894( 119909119894) 119891119874119895( 119909119895) isdom ( 119909

119895 119909119894) 119889119900119894119889119900119895

119889min (119902 119900119895) lt 119889max (119902 119900119894)

119889max (119902 119900119895) gt 119889min (119902 119900119894)

(4)

The maximum and minimum distance functions maybeintersect with each other among moving objects Two dis-tance functions of object119874

119894and119874

119895are given in Figure 4The

maximum distance of 119874119894is less than the minimum distance

of 119874119895prior to time 119905

1 so 119874

119895cannot dominate 119874

119894 119874119895might

begin to dominate119874119894from 119905

1to 1199052 as the hatched area shows

so does it from 1199053to 1199054 and from 119905

5to 1199056

4 Tracking by Events

Theprobabilistic skyline set is updated in an incremental wayThe key step is how to predict the time when the dominantrelationship changes Itrsquos hard to know the accurate timewhen119901-skyline just change But we can estimate period of timeduring which the 119901-skyline may change

41 Trigger Events As shown in Figure 4 from time 1199051to

time 1199052 the dominant relationship between 119874

119894and 119874

119895might

change because the maximum distance of 119874119894is greater than

the minimum distance of 119874119895 So we call the time between

International Journal of Distributed Sensor Networks 5

Oj

d

tqt1 t2 t3 t4 t5 t6

d (q oj)d (q oi )

d (q oi)d (q oj)

Oi

Figure 4 Transformation of dominant relationship

1199051and 119905

2an event An event on 119874

119894can be presented as

119890V119890119899119905(119900119894 119900119895) = ⟨119900

119894 119900119895 119904 119905119894119898119890 119890 119905119894119898119890⟩ where 119874

119894and 119874

119895are

two objects whose dominant relationshipmay be variedwhen119904 119905119894119898119890 and 119890 119905119894119898119890 are start time and end time of the eventrespectively

42 The Pruning Strategy for Events By analyzingrelationship of objects we know that if static charactersof any two objects 119874

119894and 119874

119895have dominant relationship

supposing that 119874119878119895≺ 119874119878

119894 an event maybe occur With the

query object moving a considerable amount of events willoccur In order to improve effectiveness of our algorithm wepropose a series of event pruning strategies

Pruning Strategy 1 If the dominant relationship in staticattributes between two moving objects 119874

119894and 119874

119895does

not exist the intersection of those two distance functionswill cause no variation to 119901-skyline set In this case theintersection will not cause any event

Proof Suppose 119900119894= (119909119894

1 119909119894

2 119909

119894

119889) 119900119895= (119909119895

1 119909119895

2 119909

119895

119889)

whose static characters are 119900119878

119894= (119909119894

1199041 119909119894

1199042 119909

119894

119904119896) and

119900119878

119895=

(119909119895

1199041 119909119895

1199042 119909

119895

119904119896) respectively It is known that the static char-

acters of119874119894and119874

119895do not possess any dominant relationship

so exist119896119901 119896119902 119909119894

119896119901gt 119909119895

119896119901

and 119909119894119896119902lt 119909119895

119896119902

Even consideringtheir dynamic attributes the dominant relationship does notexist at any time In conclusion if the dominant relationshipin static attributes between two objects does not exist theintersection of their distance functions will not cause anychange for their dominant probability Events cannot takeplace

Pruning Strategy 2 Suppose exist119900119894 119900119895 119901(119900119895≺ 119900119894) = 1

Event(119894 119895 119905begin 119905end) is an event interrelated to 119874119894and 119874

119895

If existevent(119874119894 119874119896 1199051015840

begin 1199051015840

end) (0 lt 119896 lt Num and 119896 = 119894)

and 1199051015840begin lt 119905begin the computation for event(119874119894 119874119896

1199051015840

begin 1199051015840

end) is invalid before 119905begin However if 1199051015840

end lt 119905beginevent(119894 119896 1199051015840begin 119905

1015840

end) is also invalid

Proof Because 119901(119900119895≺ 119900119894) = 1 it is known that 119901(119900

119894≺ 119900119895) = 0

prior to time 119905begin The update for event(119874119894 119874119896 1199051015840

begin 1199051015840

end) isinvalid It is also invalid when 1199051015840end lt 119905begin

5 Continuous Probabilistic SkylineQueries Algorithm

51 Initialization The initialization framework is presentedin this section Each object has static and dynamic attributesso we should compute the dominance relation on staticattributes firstly For two objects 119874

119894and 119874

119895 119874119895might

dominate 119874119894only when 119900119878

119895≺ 119900119878

119894(Algorithm 1) In order to

compute fast static skyline set denoted by 119878static is introducedif only the dominant relationship for static characters isconsidered

In any case objects move 119878static always belongs to skylineIn initialization step the moving path and distance functionof each moving object need to be precomputed according tothe information of road network and moving objects apartfrom 119878static

52 PSUR Algorithm Not all skyline probability of objectswill change at one moment If maximumminimum distancefunction of one object cuts that of others in Cartesiancoordinates skyline probability of this object maybe vary(Algorithm 2) In other words trigger events include allpossible variations of 119901-skyline for each moving object

In order to simplify the problem we suppose that allmoving objects preserve their velocity with uniform speedIf not the precomputing cannot be processed in advanceAll events should be recomputed again The movement ofmoving objects to query point can be picked up with itsshortest path to query point The intersecting time for thedistance function can be recomputed and put into eventqueue sorted by time in ascending order For each timeskyline probabilities of moving objects under trigger eventsneed to be updated

53 Algorithm Analysis and Discussion The cost incurredby our method consists of three components initializationevents computing and updating by tracking

In initialization period computing static dominant rela-tionship will cost 119874(119889 sdot 119899(119899 minus 1)2) where 119889 is staticdimensional degreeThemost cost is skyline probability com-putation The famous Simpson integration method which isintroduced to compute skyline probability of each movingobjects Num and time interval 119905 Probabilistic 119874((Lenℎ)2)where Len is uncertain segment length and ℎ is step widthof Simpson so the cost of skyline probability of each movingobject is119874((Lenℎ)2(119899minus1)) After skyline probability compu-tation judgment for 119901-skyline objects will cost 119874(119899) Above

6 International Journal of Distributed Sensor Networks

Input one query object 119899moving objectsOutput Initialization 119901-skyline(1) 119878static = NULL(2) for any point 119900

119894in 119874

(3) compute path(119900119894) get the moving path of objects

(4) compute distance(119900119894) computing distance function

(5) 119874119894= NULL

(6) for any point 119900119895(119895 = 119894) in 119874

(7) compare(119900119878119895 119900119878119894) ensure whether 119874

119895dominate 119874

119894in static attributes

(8) if 119900119878119895≺ 119900119878

119894

(9) flag(119900119895 119900119894) = 1

(10) push 119900119895into the 119874

119894

(11) else(12) flag(119900

119895 119900119894) = 0

(13) if the 119874119894= NULL

(14) 119878static = 119878static cup 119900119894

Algorithm 1 Initialization

Input the set of moving objects119863 query point 119902 119901 is the probabilistic threshold the time interval [119905119904 119905119890]

Output the 119901-Skyline at any time instant 119905 within [119905119904 119905119890]

(1) initialization()(2) compute events(3) for any point 119900

119894in 119874

(4) for each point 119900119895in 119874119894

(5) compute begin time s time and end time e time of each event(6) if s time le 119905

119890ampamp e time ge 119905

119904

(7) push it into 119876119890 valid event

(8) handle events(9) time = 119905

119904 119871119901= 119871119904

(10) while (time le 119905119890)

(11) while (119876119890= NULL)

(12) 119890 = 119876119890sdot erase() pop queuersquos head

(13) while (119890 sdot 119905begin le time)(14) 119876handle sdot push back(119890) push 119890 into queue(15) 119890 = 119876

119890sdot erase()

(16) handle(119876handle) update 119876119890 and 119878119901(17) time++

Algorithm 2 PSUR algorithm

all time cost in initialization is119874(119889sdot119899(119899minus1)2+(Lenℎ)2(119899minus1) + 119899)

In second step the worst cost of comparison for staticdominant relationship between objects is 119874(119899(119899 minus 1)2) Theinteraction time for arbitrary two moving objectsrsquo distancefunction will cost119874(120575

1) where 120575

1is constantThus it will cost

119874(1205751sdot 119899(119899 minus 1)2) in this period

Handling events generates at most 119899(119899 minus 1)2 In theworst case each event is valid in time period [119905

119904 119905119890] and

this requires (119905119890minus 119905119904) times to deal with events In every

processing skyline probability related to trigger events willcost 119874((Lenℎ)2(119899 minus 1)) while update computing for eventis 119874(120575

2) where 120575

2is constant The total cost in this period is

119874((Lenℎ)2(119899minus1)sdot(119905119890minus119905119904) sdot119899(119899minus1)2+120575

2sdot (119905119890minus119905119904) sdot119899(119899minus1)2)

In conclusion the total cost is added together for thesethree periods which is equivalent to 119874(1198992)

6 Experimental Evaluation

61 Datasets Two real road networks are used to test theeffect and efficiency of the proposed algorithm PSUR Oneis the famous seashore city Oldenburg in Germany whichincludes 6105 nodes and 7036 edges The other is Cixi city ofChina which contains 244 intersection nodes and 407 edgesmuch smaller than the first oneWe assume that the uncertainarea is segment along the road Two distributions of uniformand Gaussian distribution for probability density functionare adopted because these two functions are by far the mostimportant and commonly used in statistics Moving objectsare generated randomly Baseline and priority algorithmsproposed in [8] are used to compare with our method PSURto verify efficiency and effect The main parameters aresegment length Len static dimension number 119889 numbers of

International Journal of Distributed Sensor Networks 7

50 5000

2

4

6

8

10

12

14

N

times104

100 200 300 400

Runt

ime (

ms)

(a) Gaussian distribution

50 100 200 300 400 5000

2

4

6

8

10

12

Runt

ime (

ms)

PriorityBaseline

PSUR

N

times104

(b) Uniform distribution

Figure 5 Numbers of moving objects effects of the performance inCixi city (119889 = 5 Len = 10 and 119905 = 20)

moving objects Num and time interval 119905 and probabilisticthreshold 119901 is 05 in all experiments

We conducted our experiments on desktop PC runningon Windows XP professional The PC has Intel Core 2Duo293GHz and 3GB RAM memory All experiments werecoded in Visual C++ 2008

62 Numbers of Moving Objects In this experiment suppose119889 = 5 Len = 10 and 119905 = 20 Figure 5 shows performanceof PSUR versus baseline and priority [8] when numbersof moving objects vary on Cixirsquos road network both in

Table 2 Event size in Cixi road network (119889 = 5 Len = 10 119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 669 35

100 2721 95

200 10389 205

300 35009 400

400 62723 514

500 96890 736

Table 3 Event size in Oldenburg road network (119889 = 5 Len = 10119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 245 5

100 455 15

200 1557 41

300 3945 131

400 6464 236

500 9951 367

uniform distribution and Gaussian distribution LikewiseFigure 10 demonstrates the performance on road networkin Oldenburg The figures show that runtime increases withobjectrsquos numbers whichever the model is No matter whatmodel is used uniform or Gaussian the cost in the samedataset is similar Among these three methods the responsetime of our algorithm is only one-tenth of the other twomethods It is because baseline and priority need recomputethe probabilistic skyline set at each time while PSUR is anincremental method

If there is the same number of moving objects in tworeal networks the density of moving objects in Cixi isbigger than that in Oldenburg because Cixi is smaller thanOldenburg Therefore the chances for interaction of movingobjects in Cixi are more those that in Oldenburg Triggerevents generated in Cixi are evidently more than those inOldenburg as Tables 2 and 3 show The density of movingobjects leads to this difference because it is more sparselydistributed in Oldenburg than in Cixi for the same numberof objects As a result by observing the performance betweentwo city networks under the same data model such asFigures 5(a) and 6(a) it is noted that the runtime in thesmaller city Cixi costs a little more than that in Oldenburg

The pruning strategy has done effective work on eventsize as Tables 2 and 3 show Event size will grow withthe number of moving objects because the number of theintersection of distance function rises

63 The Effect of Uncertain Segment Length In this sectionparameters are as follows Num = 50 119889 = 5 and 119905 = 20Figures 7 and 8 show performance of three algorithms whensegment length of uncertainty varies on Cixi road network

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

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DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 3

queries in mobile environment The author in [16] focusedon the situation in which the location of a query object is notexactly known In research of skyline query field Fiedler [17]firstly proposed skyline operator on uncertain data in his dis-sertation Pei et al [18] proposed a probabilistic skylinemodelformultiinstance data where each object is part of the skylinewith a certain probability They presented two algorithmsBUM and TDM to study skyline query on uncertain data ofthe possible worldmodel (PWM) Lian andChen [19] studiedreverse-skyline queryTheymodeled the probabilistic reverseskyline query on uncertain data in both monochromaticand bichromatic case and proposed two effective pruningmethods MPRS and BPRS to reduce the search space ofquery processing Zhang et al [20] explored how to maintainskyline sets when uncertain data are updated An AR-tree isconstructed for all uncertain data and the maintenance isinserting deleting and updating on this AR-treeThe authorsin [21] designed partitioning method to compute skylineprobabilities for discrete data with uncertainty The authorsin [8] investigated skyline probabilities with a parametricform pdf (eg a Gaussian function or a Gaussian mixturemodel) The authors in [22] proposed a sliding windowskyline model to study the execution of the probabilisticskyline query over uncertain data streams [23] The authorsstudied a new problem of range-based skyline queries Twonovel algorithms I-SKY and N-SKY were presented to solvethe probabilistic and continuous range-based skyline queries

In road network Huang and Jensen [24] assumed thatthe userrsquos movement is constrained to a road network Theauthors defined route nearest-neighbour skyline queries toconsider the computation efficiency Deng et al [25] studiedmultisource skyline query in road networks Three differentroad networks ofmultisource querymethods were presentedThe authors in [26] proposed a new method to processcontinuous skyline in road network based on precomputingthe shortest range data of targets The authors in [27]introduced route skyline computation in a multiattributegraph Top routes are computed iteratively in an efficient wayand pruning technique is adopted in order to reduce thesearch space The authors in [28] focused on extracting thepath skylines and proposed PathSL to generate an optimalskyline for moving objects

In spite of much work focusing on uncertainty of skylinequeries or route skyline queries there is little work completedfor skyline query concerning uncertainty of moving objectsThe authors in [4 22ndash25] ignored the uncertainty of movingobjects while the authors [8 18 21] dealt with discrete datawith independent dominant relationship between objects Itis the first time to compute continuous probabilistic skylinequery with regard to uncertainty of moving objects in roadnetwork

3 The Probabilistic Skyline for UncertainMoving Objects

31 Skyline on Certain Points Suppose that the point setis 119878 = 119904

1 1199042 119904Num where Num is the number

of points each point in an 119899-dimensional numeric space

Table 1

Position of police car A B C D ENumber of policemen 6 6 6 4 5Equipment level 3 3 2 3 2Network distance to 119874 125 130 140 155 90

119863 = 1198891 1198892 119889

119899 The original concept of skyline is based

on the notion of dominance Let 119883 = (1199091 1199092 119909

119899) 119884 =

(1199101 1199102 119910

119899) 119883 isin 119878 119884 isin 119878 if forall119894 119909

119894le 119910119894(1 le 119894 le 119899) and

exist119895 satisfy 119909119895lt 119910119895(1 le 119895 le 119899) then 119883 is said to dominate

119884 donated by 119883 ≺ 119884 Given a set of objects 119878 an object 119883 isa skyline point if there is not any other point dominating 119883The skyline on 119878 is the set of all skyline points

32 Uncertain Model for Moving Objects After Wolfsonet al [1] firstly studied the uncertainty of moving objectsa lot of work has focused on this field [5ndash7] An uncertainregion [5] of a moving object119872119894 at time 119905 denoted by 119880119894(119905)is a closed irregular region with a velocity V such that therecorded location 119874

119894can be found only inside this region

The pdf represents the probability density distribution of anobject in its uncertain region The uncertainty pdf [5] of anobject119872119894 denoted by 119891(119900

119894) is a pdf of 119874

119894 that has a value of

0 outside 119880119894(119905)

33TheDominant Probability Whatwemainly study on is asfollows There is a set of moving target objects whose centersare 119874 = 119900

1 1199002 119900Num isin 119877

119899 and a stationary object 119902 asa query point to continuously compute updated probabilisticskyline dataset

Dissimilar to the traditional skyline query in movingenvironment the spatial location is changing with time Allattributes are divided into dynamic attributes and static onesLet us suppose that there are 119898 dynamic attributes 119896 staticattributes and 119899 attributes where 119899 = 119898 + 119896 For each object119874119894= (119909119894

1 119909119894

2 119909

119894

119889)119879 the static attributes construct a vector

denoted by119874119878119894= (119909119894

1198781 119909119894

1198782 119909

119894

119878119896)119879 while the dynamic ones

are made up of a vector 119874119889119894= (119909119894

1198891 119909119894

1198892 119909

119894

119889119898)119879 where

119899 = 119896+119898 For instance in Figure 1 the number of police andequipment level belong to static attributes because they areinvariant in our study case However the distance from119874

119894to

119902 is varying continuously with police car119874119894moving In order

to simplify the description dynamic attributes are supposedto include only spatial position (Table 1)

Definition 1 (dominant probability) Let 119874119894 119874119895be two mov-

ing objects with uncertainty and 119902 be a stationary query pointThen probability that 119874

119895dominates 119874

119894is

119901 (119900119895≺ 119900119894)

= int119880119903119874119895

int119880119903119874119894

119891119874119894( 119909119894) 119891119874119895( 119909119895) isdom ( 119909

119895 119909119894) 119889119900119894119889119900119895

(1)

where 119891119874119894( 119909119894) and 119891

119874119895( 119909119895) are probability density function of

object 119874119894and 119874

119895 119909119895isin 119880119903(119874

119895) 119909119894isin 119880119903(119874

119894) and function

4 International Journal of Distributed Sensor Networks

q

Oj

xj

xi

Ur(Oj)

Oi

Ur(Oi)

Figure 2 Dominant probability

isdom ( 119909119895 119909119894) =

1 dist( 119909119895 119902)ledist( 119909119894 119902)0 otherwise dist( 119909

119895 119902) is

Euclidean distance between 119909119895and 119902

According to the definition of dominance in (1) wemaintain that 119874

119895can have dominance probability on 119874

119894only

if the static attributes of 119874119895dominate the static ones of 119874

119894

As shown in Figure 2 for arbitrary point 119909119895in 119880119903(119874

119895) each

point 119909119894in119880119903(119874

119894) that satisfies dist( 119909

119895 119902) le dist( 119909

119894 119902)will be

dominated by 119909119895 as the hatched area shows

34 The Skyline Probability

Definition 2 (skyline probability) The skyline probability ofobject 119874

119894is the likelihood that object 119874

119894is not dominated by

any other object and is defined below

Pr (119900119894) = Pr( and

119874119895isin119874

119874119895 ≺ 119874119894)

= int119880119903119874119894

119891119874119894( 119909119894)

timesprod(1 minus int119891119874119895( 119909119895) isdom ( 119909

119894 119909119895) 119889119900119895)119889119900119894

(2)

where 119891119874119894( 119909119894) and 119891

119874119895( 119909119895) are probability density function of

object 119874119894and 119874

119895 respectively 119909

119895isin 119880119903(119874

119895) 119909119894isin 119880119903(119874

119894)

Definition 3 (119901-skyline) Let 119901 isin [0 sdot sdot sdot 1] be a threshold The119901-skyline is the set of objects for which the following propertyholds

119878120591= 119874119894isin 119874 | Pr (119874

119894) ge 119901 (3)

35 UncertainModel in RoadNetwork The road network canbe treated as a nondirection graph 119866 = ⟨119881 119864119882⟩ where 119881 isnode set representing crossroad 119864 is edge representing roadsbetween two crossroads and119882 is length of 119864

r Coi

UI(t)

A(t)

Figure 3 Uncertain model in road network

In road network the objects are limited movement sothe uncertain domain is denoted by a line segment with 119891(119905)distribution which 119891(119905) is pdf as Figure 3 shows

Denote 119889(V V1015840) by the shortest path between nodes V andV1015840 119889(V V1015840) = infin if there exists no path from V to V1015840 In roadnetwork the distance is represented by shortest path

Definition 4 (minimum distance function) The minimumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889min(119902 119900119894) = 119889(119902 119900119894) minus 119903

Definition 5 (maximum distance function) The maximumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889max(119902 119900119894) = 119889(119902 119900119894) + 119903

In continuous movement the dominant relationship oftwo objects will change For two moving objects 119874

119894and 119874

119895

119901 (119900119895≺ 119900119894)

=

1

119889max (119902 119900119895) le 119889min (119902 119900119894)

0

119889min (119902 119900119895) ge 119889max (119902 119900119894)

int119880119903119874119895

int119880119903119874119894

119891119874119894( 119909119894) 119891119874119895( 119909119895) isdom ( 119909

119895 119909119894) 119889119900119894119889119900119895

119889min (119902 119900119895) lt 119889max (119902 119900119894)

119889max (119902 119900119895) gt 119889min (119902 119900119894)

(4)

The maximum and minimum distance functions maybeintersect with each other among moving objects Two dis-tance functions of object119874

119894and119874

119895are given in Figure 4The

maximum distance of 119874119894is less than the minimum distance

of 119874119895prior to time 119905

1 so 119874

119895cannot dominate 119874

119894 119874119895might

begin to dominate119874119894from 119905

1to 1199052 as the hatched area shows

so does it from 1199053to 1199054 and from 119905

5to 1199056

4 Tracking by Events

Theprobabilistic skyline set is updated in an incremental wayThe key step is how to predict the time when the dominantrelationship changes Itrsquos hard to know the accurate timewhen119901-skyline just change But we can estimate period of timeduring which the 119901-skyline may change

41 Trigger Events As shown in Figure 4 from time 1199051to

time 1199052 the dominant relationship between 119874

119894and 119874

119895might

change because the maximum distance of 119874119894is greater than

the minimum distance of 119874119895 So we call the time between

International Journal of Distributed Sensor Networks 5

Oj

d

tqt1 t2 t3 t4 t5 t6

d (q oj)d (q oi )

d (q oi)d (q oj)

Oi

Figure 4 Transformation of dominant relationship

1199051and 119905

2an event An event on 119874

119894can be presented as

119890V119890119899119905(119900119894 119900119895) = ⟨119900

119894 119900119895 119904 119905119894119898119890 119890 119905119894119898119890⟩ where 119874

119894and 119874

119895are

two objects whose dominant relationshipmay be variedwhen119904 119905119894119898119890 and 119890 119905119894119898119890 are start time and end time of the eventrespectively

42 The Pruning Strategy for Events By analyzingrelationship of objects we know that if static charactersof any two objects 119874

119894and 119874

119895have dominant relationship

supposing that 119874119878119895≺ 119874119878

119894 an event maybe occur With the

query object moving a considerable amount of events willoccur In order to improve effectiveness of our algorithm wepropose a series of event pruning strategies

Pruning Strategy 1 If the dominant relationship in staticattributes between two moving objects 119874

119894and 119874

119895does

not exist the intersection of those two distance functionswill cause no variation to 119901-skyline set In this case theintersection will not cause any event

Proof Suppose 119900119894= (119909119894

1 119909119894

2 119909

119894

119889) 119900119895= (119909119895

1 119909119895

2 119909

119895

119889)

whose static characters are 119900119878

119894= (119909119894

1199041 119909119894

1199042 119909

119894

119904119896) and

119900119878

119895=

(119909119895

1199041 119909119895

1199042 119909

119895

119904119896) respectively It is known that the static char-

acters of119874119894and119874

119895do not possess any dominant relationship

so exist119896119901 119896119902 119909119894

119896119901gt 119909119895

119896119901

and 119909119894119896119902lt 119909119895

119896119902

Even consideringtheir dynamic attributes the dominant relationship does notexist at any time In conclusion if the dominant relationshipin static attributes between two objects does not exist theintersection of their distance functions will not cause anychange for their dominant probability Events cannot takeplace

Pruning Strategy 2 Suppose exist119900119894 119900119895 119901(119900119895≺ 119900119894) = 1

Event(119894 119895 119905begin 119905end) is an event interrelated to 119874119894and 119874

119895

If existevent(119874119894 119874119896 1199051015840

begin 1199051015840

end) (0 lt 119896 lt Num and 119896 = 119894)

and 1199051015840begin lt 119905begin the computation for event(119874119894 119874119896

1199051015840

begin 1199051015840

end) is invalid before 119905begin However if 1199051015840

end lt 119905beginevent(119894 119896 1199051015840begin 119905

1015840

end) is also invalid

Proof Because 119901(119900119895≺ 119900119894) = 1 it is known that 119901(119900

119894≺ 119900119895) = 0

prior to time 119905begin The update for event(119874119894 119874119896 1199051015840

begin 1199051015840

end) isinvalid It is also invalid when 1199051015840end lt 119905begin

5 Continuous Probabilistic SkylineQueries Algorithm

51 Initialization The initialization framework is presentedin this section Each object has static and dynamic attributesso we should compute the dominance relation on staticattributes firstly For two objects 119874

119894and 119874

119895 119874119895might

dominate 119874119894only when 119900119878

119895≺ 119900119878

119894(Algorithm 1) In order to

compute fast static skyline set denoted by 119878static is introducedif only the dominant relationship for static characters isconsidered

In any case objects move 119878static always belongs to skylineIn initialization step the moving path and distance functionof each moving object need to be precomputed according tothe information of road network and moving objects apartfrom 119878static

52 PSUR Algorithm Not all skyline probability of objectswill change at one moment If maximumminimum distancefunction of one object cuts that of others in Cartesiancoordinates skyline probability of this object maybe vary(Algorithm 2) In other words trigger events include allpossible variations of 119901-skyline for each moving object

In order to simplify the problem we suppose that allmoving objects preserve their velocity with uniform speedIf not the precomputing cannot be processed in advanceAll events should be recomputed again The movement ofmoving objects to query point can be picked up with itsshortest path to query point The intersecting time for thedistance function can be recomputed and put into eventqueue sorted by time in ascending order For each timeskyline probabilities of moving objects under trigger eventsneed to be updated

53 Algorithm Analysis and Discussion The cost incurredby our method consists of three components initializationevents computing and updating by tracking

In initialization period computing static dominant rela-tionship will cost 119874(119889 sdot 119899(119899 minus 1)2) where 119889 is staticdimensional degreeThemost cost is skyline probability com-putation The famous Simpson integration method which isintroduced to compute skyline probability of each movingobjects Num and time interval 119905 Probabilistic 119874((Lenℎ)2)where Len is uncertain segment length and ℎ is step widthof Simpson so the cost of skyline probability of each movingobject is119874((Lenℎ)2(119899minus1)) After skyline probability compu-tation judgment for 119901-skyline objects will cost 119874(119899) Above

6 International Journal of Distributed Sensor Networks

Input one query object 119899moving objectsOutput Initialization 119901-skyline(1) 119878static = NULL(2) for any point 119900

119894in 119874

(3) compute path(119900119894) get the moving path of objects

(4) compute distance(119900119894) computing distance function

(5) 119874119894= NULL

(6) for any point 119900119895(119895 = 119894) in 119874

(7) compare(119900119878119895 119900119878119894) ensure whether 119874

119895dominate 119874

119894in static attributes

(8) if 119900119878119895≺ 119900119878

119894

(9) flag(119900119895 119900119894) = 1

(10) push 119900119895into the 119874

119894

(11) else(12) flag(119900

119895 119900119894) = 0

(13) if the 119874119894= NULL

(14) 119878static = 119878static cup 119900119894

Algorithm 1 Initialization

Input the set of moving objects119863 query point 119902 119901 is the probabilistic threshold the time interval [119905119904 119905119890]

Output the 119901-Skyline at any time instant 119905 within [119905119904 119905119890]

(1) initialization()(2) compute events(3) for any point 119900

119894in 119874

(4) for each point 119900119895in 119874119894

(5) compute begin time s time and end time e time of each event(6) if s time le 119905

119890ampamp e time ge 119905

119904

(7) push it into 119876119890 valid event

(8) handle events(9) time = 119905

119904 119871119901= 119871119904

(10) while (time le 119905119890)

(11) while (119876119890= NULL)

(12) 119890 = 119876119890sdot erase() pop queuersquos head

(13) while (119890 sdot 119905begin le time)(14) 119876handle sdot push back(119890) push 119890 into queue(15) 119890 = 119876

119890sdot erase()

(16) handle(119876handle) update 119876119890 and 119878119901(17) time++

Algorithm 2 PSUR algorithm

all time cost in initialization is119874(119889sdot119899(119899minus1)2+(Lenℎ)2(119899minus1) + 119899)

In second step the worst cost of comparison for staticdominant relationship between objects is 119874(119899(119899 minus 1)2) Theinteraction time for arbitrary two moving objectsrsquo distancefunction will cost119874(120575

1) where 120575

1is constantThus it will cost

119874(1205751sdot 119899(119899 minus 1)2) in this period

Handling events generates at most 119899(119899 minus 1)2 In theworst case each event is valid in time period [119905

119904 119905119890] and

this requires (119905119890minus 119905119904) times to deal with events In every

processing skyline probability related to trigger events willcost 119874((Lenℎ)2(119899 minus 1)) while update computing for eventis 119874(120575

2) where 120575

2is constant The total cost in this period is

119874((Lenℎ)2(119899minus1)sdot(119905119890minus119905119904) sdot119899(119899minus1)2+120575

2sdot (119905119890minus119905119904) sdot119899(119899minus1)2)

In conclusion the total cost is added together for thesethree periods which is equivalent to 119874(1198992)

6 Experimental Evaluation

61 Datasets Two real road networks are used to test theeffect and efficiency of the proposed algorithm PSUR Oneis the famous seashore city Oldenburg in Germany whichincludes 6105 nodes and 7036 edges The other is Cixi city ofChina which contains 244 intersection nodes and 407 edgesmuch smaller than the first oneWe assume that the uncertainarea is segment along the road Two distributions of uniformand Gaussian distribution for probability density functionare adopted because these two functions are by far the mostimportant and commonly used in statistics Moving objectsare generated randomly Baseline and priority algorithmsproposed in [8] are used to compare with our method PSURto verify efficiency and effect The main parameters aresegment length Len static dimension number 119889 numbers of

International Journal of Distributed Sensor Networks 7

50 5000

2

4

6

8

10

12

14

N

times104

100 200 300 400

Runt

ime (

ms)

(a) Gaussian distribution

50 100 200 300 400 5000

2

4

6

8

10

12

Runt

ime (

ms)

PriorityBaseline

PSUR

N

times104

(b) Uniform distribution

Figure 5 Numbers of moving objects effects of the performance inCixi city (119889 = 5 Len = 10 and 119905 = 20)

moving objects Num and time interval 119905 and probabilisticthreshold 119901 is 05 in all experiments

We conducted our experiments on desktop PC runningon Windows XP professional The PC has Intel Core 2Duo293GHz and 3GB RAM memory All experiments werecoded in Visual C++ 2008

62 Numbers of Moving Objects In this experiment suppose119889 = 5 Len = 10 and 119905 = 20 Figure 5 shows performanceof PSUR versus baseline and priority [8] when numbersof moving objects vary on Cixirsquos road network both in

Table 2 Event size in Cixi road network (119889 = 5 Len = 10 119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 669 35

100 2721 95

200 10389 205

300 35009 400

400 62723 514

500 96890 736

Table 3 Event size in Oldenburg road network (119889 = 5 Len = 10119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 245 5

100 455 15

200 1557 41

300 3945 131

400 6464 236

500 9951 367

uniform distribution and Gaussian distribution LikewiseFigure 10 demonstrates the performance on road networkin Oldenburg The figures show that runtime increases withobjectrsquos numbers whichever the model is No matter whatmodel is used uniform or Gaussian the cost in the samedataset is similar Among these three methods the responsetime of our algorithm is only one-tenth of the other twomethods It is because baseline and priority need recomputethe probabilistic skyline set at each time while PSUR is anincremental method

If there is the same number of moving objects in tworeal networks the density of moving objects in Cixi isbigger than that in Oldenburg because Cixi is smaller thanOldenburg Therefore the chances for interaction of movingobjects in Cixi are more those that in Oldenburg Triggerevents generated in Cixi are evidently more than those inOldenburg as Tables 2 and 3 show The density of movingobjects leads to this difference because it is more sparselydistributed in Oldenburg than in Cixi for the same numberof objects As a result by observing the performance betweentwo city networks under the same data model such asFigures 5(a) and 6(a) it is noted that the runtime in thesmaller city Cixi costs a little more than that in Oldenburg

The pruning strategy has done effective work on eventsize as Tables 2 and 3 show Event size will grow withthe number of moving objects because the number of theintersection of distance function rises

63 The Effect of Uncertain Segment Length In this sectionparameters are as follows Num = 50 119889 = 5 and 119905 = 20Figures 7 and 8 show performance of three algorithms whensegment length of uncertainty varies on Cixi road network

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 International Journal of Distributed Sensor Networks

q

Oj

xj

xi

Ur(Oj)

Oi

Ur(Oi)

Figure 2 Dominant probability

isdom ( 119909119895 119909119894) =

1 dist( 119909119895 119902)ledist( 119909119894 119902)0 otherwise dist( 119909

119895 119902) is

Euclidean distance between 119909119895and 119902

According to the definition of dominance in (1) wemaintain that 119874

119895can have dominance probability on 119874

119894only

if the static attributes of 119874119895dominate the static ones of 119874

119894

As shown in Figure 2 for arbitrary point 119909119895in 119880119903(119874

119895) each

point 119909119894in119880119903(119874

119894) that satisfies dist( 119909

119895 119902) le dist( 119909

119894 119902)will be

dominated by 119909119895 as the hatched area shows

34 The Skyline Probability

Definition 2 (skyline probability) The skyline probability ofobject 119874

119894is the likelihood that object 119874

119894is not dominated by

any other object and is defined below

Pr (119900119894) = Pr( and

119874119895isin119874

119874119895 ≺ 119874119894)

= int119880119903119874119894

119891119874119894( 119909119894)

timesprod(1 minus int119891119874119895( 119909119895) isdom ( 119909

119894 119909119895) 119889119900119895)119889119900119894

(2)

where 119891119874119894( 119909119894) and 119891

119874119895( 119909119895) are probability density function of

object 119874119894and 119874

119895 respectively 119909

119895isin 119880119903(119874

119895) 119909119894isin 119880119903(119874

119894)

Definition 3 (119901-skyline) Let 119901 isin [0 sdot sdot sdot 1] be a threshold The119901-skyline is the set of objects for which the following propertyholds

119878120591= 119874119894isin 119874 | Pr (119874

119894) ge 119901 (3)

35 UncertainModel in RoadNetwork The road network canbe treated as a nondirection graph 119866 = ⟨119881 119864119882⟩ where 119881 isnode set representing crossroad 119864 is edge representing roadsbetween two crossroads and119882 is length of 119864

r Coi

UI(t)

A(t)

Figure 3 Uncertain model in road network

In road network the objects are limited movement sothe uncertain domain is denoted by a line segment with 119891(119905)distribution which 119891(119905) is pdf as Figure 3 shows

Denote 119889(V V1015840) by the shortest path between nodes V andV1015840 119889(V V1015840) = infin if there exists no path from V to V1015840 In roadnetwork the distance is represented by shortest path

Definition 4 (minimum distance function) The minimumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889min(119902 119900119894) = 119889(119902 119900119894) minus 119903

Definition 5 (maximum distance function) The maximumdistance between uncertain object 119874

119894to query 119902 at time 119905 is

denoted by 119889max(119902 119900119894) = 119889(119902 119900119894) + 119903

In continuous movement the dominant relationship oftwo objects will change For two moving objects 119874

119894and 119874

119895

119901 (119900119895≺ 119900119894)

=

1

119889max (119902 119900119895) le 119889min (119902 119900119894)

0

119889min (119902 119900119895) ge 119889max (119902 119900119894)

int119880119903119874119895

int119880119903119874119894

119891119874119894( 119909119894) 119891119874119895( 119909119895) isdom ( 119909

119895 119909119894) 119889119900119894119889119900119895

119889min (119902 119900119895) lt 119889max (119902 119900119894)

119889max (119902 119900119895) gt 119889min (119902 119900119894)

(4)

The maximum and minimum distance functions maybeintersect with each other among moving objects Two dis-tance functions of object119874

119894and119874

119895are given in Figure 4The

maximum distance of 119874119894is less than the minimum distance

of 119874119895prior to time 119905

1 so 119874

119895cannot dominate 119874

119894 119874119895might

begin to dominate119874119894from 119905

1to 1199052 as the hatched area shows

so does it from 1199053to 1199054 and from 119905

5to 1199056

4 Tracking by Events

Theprobabilistic skyline set is updated in an incremental wayThe key step is how to predict the time when the dominantrelationship changes Itrsquos hard to know the accurate timewhen119901-skyline just change But we can estimate period of timeduring which the 119901-skyline may change

41 Trigger Events As shown in Figure 4 from time 1199051to

time 1199052 the dominant relationship between 119874

119894and 119874

119895might

change because the maximum distance of 119874119894is greater than

the minimum distance of 119874119895 So we call the time between

International Journal of Distributed Sensor Networks 5

Oj

d

tqt1 t2 t3 t4 t5 t6

d (q oj)d (q oi )

d (q oi)d (q oj)

Oi

Figure 4 Transformation of dominant relationship

1199051and 119905

2an event An event on 119874

119894can be presented as

119890V119890119899119905(119900119894 119900119895) = ⟨119900

119894 119900119895 119904 119905119894119898119890 119890 119905119894119898119890⟩ where 119874

119894and 119874

119895are

two objects whose dominant relationshipmay be variedwhen119904 119905119894119898119890 and 119890 119905119894119898119890 are start time and end time of the eventrespectively

42 The Pruning Strategy for Events By analyzingrelationship of objects we know that if static charactersof any two objects 119874

119894and 119874

119895have dominant relationship

supposing that 119874119878119895≺ 119874119878

119894 an event maybe occur With the

query object moving a considerable amount of events willoccur In order to improve effectiveness of our algorithm wepropose a series of event pruning strategies

Pruning Strategy 1 If the dominant relationship in staticattributes between two moving objects 119874

119894and 119874

119895does

not exist the intersection of those two distance functionswill cause no variation to 119901-skyline set In this case theintersection will not cause any event

Proof Suppose 119900119894= (119909119894

1 119909119894

2 119909

119894

119889) 119900119895= (119909119895

1 119909119895

2 119909

119895

119889)

whose static characters are 119900119878

119894= (119909119894

1199041 119909119894

1199042 119909

119894

119904119896) and

119900119878

119895=

(119909119895

1199041 119909119895

1199042 119909

119895

119904119896) respectively It is known that the static char-

acters of119874119894and119874

119895do not possess any dominant relationship

so exist119896119901 119896119902 119909119894

119896119901gt 119909119895

119896119901

and 119909119894119896119902lt 119909119895

119896119902

Even consideringtheir dynamic attributes the dominant relationship does notexist at any time In conclusion if the dominant relationshipin static attributes between two objects does not exist theintersection of their distance functions will not cause anychange for their dominant probability Events cannot takeplace

Pruning Strategy 2 Suppose exist119900119894 119900119895 119901(119900119895≺ 119900119894) = 1

Event(119894 119895 119905begin 119905end) is an event interrelated to 119874119894and 119874

119895

If existevent(119874119894 119874119896 1199051015840

begin 1199051015840

end) (0 lt 119896 lt Num and 119896 = 119894)

and 1199051015840begin lt 119905begin the computation for event(119874119894 119874119896

1199051015840

begin 1199051015840

end) is invalid before 119905begin However if 1199051015840

end lt 119905beginevent(119894 119896 1199051015840begin 119905

1015840

end) is also invalid

Proof Because 119901(119900119895≺ 119900119894) = 1 it is known that 119901(119900

119894≺ 119900119895) = 0

prior to time 119905begin The update for event(119874119894 119874119896 1199051015840

begin 1199051015840

end) isinvalid It is also invalid when 1199051015840end lt 119905begin

5 Continuous Probabilistic SkylineQueries Algorithm

51 Initialization The initialization framework is presentedin this section Each object has static and dynamic attributesso we should compute the dominance relation on staticattributes firstly For two objects 119874

119894and 119874

119895 119874119895might

dominate 119874119894only when 119900119878

119895≺ 119900119878

119894(Algorithm 1) In order to

compute fast static skyline set denoted by 119878static is introducedif only the dominant relationship for static characters isconsidered

In any case objects move 119878static always belongs to skylineIn initialization step the moving path and distance functionof each moving object need to be precomputed according tothe information of road network and moving objects apartfrom 119878static

52 PSUR Algorithm Not all skyline probability of objectswill change at one moment If maximumminimum distancefunction of one object cuts that of others in Cartesiancoordinates skyline probability of this object maybe vary(Algorithm 2) In other words trigger events include allpossible variations of 119901-skyline for each moving object

In order to simplify the problem we suppose that allmoving objects preserve their velocity with uniform speedIf not the precomputing cannot be processed in advanceAll events should be recomputed again The movement ofmoving objects to query point can be picked up with itsshortest path to query point The intersecting time for thedistance function can be recomputed and put into eventqueue sorted by time in ascending order For each timeskyline probabilities of moving objects under trigger eventsneed to be updated

53 Algorithm Analysis and Discussion The cost incurredby our method consists of three components initializationevents computing and updating by tracking

In initialization period computing static dominant rela-tionship will cost 119874(119889 sdot 119899(119899 minus 1)2) where 119889 is staticdimensional degreeThemost cost is skyline probability com-putation The famous Simpson integration method which isintroduced to compute skyline probability of each movingobjects Num and time interval 119905 Probabilistic 119874((Lenℎ)2)where Len is uncertain segment length and ℎ is step widthof Simpson so the cost of skyline probability of each movingobject is119874((Lenℎ)2(119899minus1)) After skyline probability compu-tation judgment for 119901-skyline objects will cost 119874(119899) Above

6 International Journal of Distributed Sensor Networks

Input one query object 119899moving objectsOutput Initialization 119901-skyline(1) 119878static = NULL(2) for any point 119900

119894in 119874

(3) compute path(119900119894) get the moving path of objects

(4) compute distance(119900119894) computing distance function

(5) 119874119894= NULL

(6) for any point 119900119895(119895 = 119894) in 119874

(7) compare(119900119878119895 119900119878119894) ensure whether 119874

119895dominate 119874

119894in static attributes

(8) if 119900119878119895≺ 119900119878

119894

(9) flag(119900119895 119900119894) = 1

(10) push 119900119895into the 119874

119894

(11) else(12) flag(119900

119895 119900119894) = 0

(13) if the 119874119894= NULL

(14) 119878static = 119878static cup 119900119894

Algorithm 1 Initialization

Input the set of moving objects119863 query point 119902 119901 is the probabilistic threshold the time interval [119905119904 119905119890]

Output the 119901-Skyline at any time instant 119905 within [119905119904 119905119890]

(1) initialization()(2) compute events(3) for any point 119900

119894in 119874

(4) for each point 119900119895in 119874119894

(5) compute begin time s time and end time e time of each event(6) if s time le 119905

119890ampamp e time ge 119905

119904

(7) push it into 119876119890 valid event

(8) handle events(9) time = 119905

119904 119871119901= 119871119904

(10) while (time le 119905119890)

(11) while (119876119890= NULL)

(12) 119890 = 119876119890sdot erase() pop queuersquos head

(13) while (119890 sdot 119905begin le time)(14) 119876handle sdot push back(119890) push 119890 into queue(15) 119890 = 119876

119890sdot erase()

(16) handle(119876handle) update 119876119890 and 119878119901(17) time++

Algorithm 2 PSUR algorithm

all time cost in initialization is119874(119889sdot119899(119899minus1)2+(Lenℎ)2(119899minus1) + 119899)

In second step the worst cost of comparison for staticdominant relationship between objects is 119874(119899(119899 minus 1)2) Theinteraction time for arbitrary two moving objectsrsquo distancefunction will cost119874(120575

1) where 120575

1is constantThus it will cost

119874(1205751sdot 119899(119899 minus 1)2) in this period

Handling events generates at most 119899(119899 minus 1)2 In theworst case each event is valid in time period [119905

119904 119905119890] and

this requires (119905119890minus 119905119904) times to deal with events In every

processing skyline probability related to trigger events willcost 119874((Lenℎ)2(119899 minus 1)) while update computing for eventis 119874(120575

2) where 120575

2is constant The total cost in this period is

119874((Lenℎ)2(119899minus1)sdot(119905119890minus119905119904) sdot119899(119899minus1)2+120575

2sdot (119905119890minus119905119904) sdot119899(119899minus1)2)

In conclusion the total cost is added together for thesethree periods which is equivalent to 119874(1198992)

6 Experimental Evaluation

61 Datasets Two real road networks are used to test theeffect and efficiency of the proposed algorithm PSUR Oneis the famous seashore city Oldenburg in Germany whichincludes 6105 nodes and 7036 edges The other is Cixi city ofChina which contains 244 intersection nodes and 407 edgesmuch smaller than the first oneWe assume that the uncertainarea is segment along the road Two distributions of uniformand Gaussian distribution for probability density functionare adopted because these two functions are by far the mostimportant and commonly used in statistics Moving objectsare generated randomly Baseline and priority algorithmsproposed in [8] are used to compare with our method PSURto verify efficiency and effect The main parameters aresegment length Len static dimension number 119889 numbers of

International Journal of Distributed Sensor Networks 7

50 5000

2

4

6

8

10

12

14

N

times104

100 200 300 400

Runt

ime (

ms)

(a) Gaussian distribution

50 100 200 300 400 5000

2

4

6

8

10

12

Runt

ime (

ms)

PriorityBaseline

PSUR

N

times104

(b) Uniform distribution

Figure 5 Numbers of moving objects effects of the performance inCixi city (119889 = 5 Len = 10 and 119905 = 20)

moving objects Num and time interval 119905 and probabilisticthreshold 119901 is 05 in all experiments

We conducted our experiments on desktop PC runningon Windows XP professional The PC has Intel Core 2Duo293GHz and 3GB RAM memory All experiments werecoded in Visual C++ 2008

62 Numbers of Moving Objects In this experiment suppose119889 = 5 Len = 10 and 119905 = 20 Figure 5 shows performanceof PSUR versus baseline and priority [8] when numbersof moving objects vary on Cixirsquos road network both in

Table 2 Event size in Cixi road network (119889 = 5 Len = 10 119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 669 35

100 2721 95

200 10389 205

300 35009 400

400 62723 514

500 96890 736

Table 3 Event size in Oldenburg road network (119889 = 5 Len = 10119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 245 5

100 455 15

200 1557 41

300 3945 131

400 6464 236

500 9951 367

uniform distribution and Gaussian distribution LikewiseFigure 10 demonstrates the performance on road networkin Oldenburg The figures show that runtime increases withobjectrsquos numbers whichever the model is No matter whatmodel is used uniform or Gaussian the cost in the samedataset is similar Among these three methods the responsetime of our algorithm is only one-tenth of the other twomethods It is because baseline and priority need recomputethe probabilistic skyline set at each time while PSUR is anincremental method

If there is the same number of moving objects in tworeal networks the density of moving objects in Cixi isbigger than that in Oldenburg because Cixi is smaller thanOldenburg Therefore the chances for interaction of movingobjects in Cixi are more those that in Oldenburg Triggerevents generated in Cixi are evidently more than those inOldenburg as Tables 2 and 3 show The density of movingobjects leads to this difference because it is more sparselydistributed in Oldenburg than in Cixi for the same numberof objects As a result by observing the performance betweentwo city networks under the same data model such asFigures 5(a) and 6(a) it is noted that the runtime in thesmaller city Cixi costs a little more than that in Oldenburg

The pruning strategy has done effective work on eventsize as Tables 2 and 3 show Event size will grow withthe number of moving objects because the number of theintersection of distance function rises

63 The Effect of Uncertain Segment Length In this sectionparameters are as follows Num = 50 119889 = 5 and 119905 = 20Figures 7 and 8 show performance of three algorithms whensegment length of uncertainty varies on Cixi road network

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 5

Oj

d

tqt1 t2 t3 t4 t5 t6

d (q oj)d (q oi )

d (q oi)d (q oj)

Oi

Figure 4 Transformation of dominant relationship

1199051and 119905

2an event An event on 119874

119894can be presented as

119890V119890119899119905(119900119894 119900119895) = ⟨119900

119894 119900119895 119904 119905119894119898119890 119890 119905119894119898119890⟩ where 119874

119894and 119874

119895are

two objects whose dominant relationshipmay be variedwhen119904 119905119894119898119890 and 119890 119905119894119898119890 are start time and end time of the eventrespectively

42 The Pruning Strategy for Events By analyzingrelationship of objects we know that if static charactersof any two objects 119874

119894and 119874

119895have dominant relationship

supposing that 119874119878119895≺ 119874119878

119894 an event maybe occur With the

query object moving a considerable amount of events willoccur In order to improve effectiveness of our algorithm wepropose a series of event pruning strategies

Pruning Strategy 1 If the dominant relationship in staticattributes between two moving objects 119874

119894and 119874

119895does

not exist the intersection of those two distance functionswill cause no variation to 119901-skyline set In this case theintersection will not cause any event

Proof Suppose 119900119894= (119909119894

1 119909119894

2 119909

119894

119889) 119900119895= (119909119895

1 119909119895

2 119909

119895

119889)

whose static characters are 119900119878

119894= (119909119894

1199041 119909119894

1199042 119909

119894

119904119896) and

119900119878

119895=

(119909119895

1199041 119909119895

1199042 119909

119895

119904119896) respectively It is known that the static char-

acters of119874119894and119874

119895do not possess any dominant relationship

so exist119896119901 119896119902 119909119894

119896119901gt 119909119895

119896119901

and 119909119894119896119902lt 119909119895

119896119902

Even consideringtheir dynamic attributes the dominant relationship does notexist at any time In conclusion if the dominant relationshipin static attributes between two objects does not exist theintersection of their distance functions will not cause anychange for their dominant probability Events cannot takeplace

Pruning Strategy 2 Suppose exist119900119894 119900119895 119901(119900119895≺ 119900119894) = 1

Event(119894 119895 119905begin 119905end) is an event interrelated to 119874119894and 119874

119895

If existevent(119874119894 119874119896 1199051015840

begin 1199051015840

end) (0 lt 119896 lt Num and 119896 = 119894)

and 1199051015840begin lt 119905begin the computation for event(119874119894 119874119896

1199051015840

begin 1199051015840

end) is invalid before 119905begin However if 1199051015840

end lt 119905beginevent(119894 119896 1199051015840begin 119905

1015840

end) is also invalid

Proof Because 119901(119900119895≺ 119900119894) = 1 it is known that 119901(119900

119894≺ 119900119895) = 0

prior to time 119905begin The update for event(119874119894 119874119896 1199051015840

begin 1199051015840

end) isinvalid It is also invalid when 1199051015840end lt 119905begin

5 Continuous Probabilistic SkylineQueries Algorithm

51 Initialization The initialization framework is presentedin this section Each object has static and dynamic attributesso we should compute the dominance relation on staticattributes firstly For two objects 119874

119894and 119874

119895 119874119895might

dominate 119874119894only when 119900119878

119895≺ 119900119878

119894(Algorithm 1) In order to

compute fast static skyline set denoted by 119878static is introducedif only the dominant relationship for static characters isconsidered

In any case objects move 119878static always belongs to skylineIn initialization step the moving path and distance functionof each moving object need to be precomputed according tothe information of road network and moving objects apartfrom 119878static

52 PSUR Algorithm Not all skyline probability of objectswill change at one moment If maximumminimum distancefunction of one object cuts that of others in Cartesiancoordinates skyline probability of this object maybe vary(Algorithm 2) In other words trigger events include allpossible variations of 119901-skyline for each moving object

In order to simplify the problem we suppose that allmoving objects preserve their velocity with uniform speedIf not the precomputing cannot be processed in advanceAll events should be recomputed again The movement ofmoving objects to query point can be picked up with itsshortest path to query point The intersecting time for thedistance function can be recomputed and put into eventqueue sorted by time in ascending order For each timeskyline probabilities of moving objects under trigger eventsneed to be updated

53 Algorithm Analysis and Discussion The cost incurredby our method consists of three components initializationevents computing and updating by tracking

In initialization period computing static dominant rela-tionship will cost 119874(119889 sdot 119899(119899 minus 1)2) where 119889 is staticdimensional degreeThemost cost is skyline probability com-putation The famous Simpson integration method which isintroduced to compute skyline probability of each movingobjects Num and time interval 119905 Probabilistic 119874((Lenℎ)2)where Len is uncertain segment length and ℎ is step widthof Simpson so the cost of skyline probability of each movingobject is119874((Lenℎ)2(119899minus1)) After skyline probability compu-tation judgment for 119901-skyline objects will cost 119874(119899) Above

6 International Journal of Distributed Sensor Networks

Input one query object 119899moving objectsOutput Initialization 119901-skyline(1) 119878static = NULL(2) for any point 119900

119894in 119874

(3) compute path(119900119894) get the moving path of objects

(4) compute distance(119900119894) computing distance function

(5) 119874119894= NULL

(6) for any point 119900119895(119895 = 119894) in 119874

(7) compare(119900119878119895 119900119878119894) ensure whether 119874

119895dominate 119874

119894in static attributes

(8) if 119900119878119895≺ 119900119878

119894

(9) flag(119900119895 119900119894) = 1

(10) push 119900119895into the 119874

119894

(11) else(12) flag(119900

119895 119900119894) = 0

(13) if the 119874119894= NULL

(14) 119878static = 119878static cup 119900119894

Algorithm 1 Initialization

Input the set of moving objects119863 query point 119902 119901 is the probabilistic threshold the time interval [119905119904 119905119890]

Output the 119901-Skyline at any time instant 119905 within [119905119904 119905119890]

(1) initialization()(2) compute events(3) for any point 119900

119894in 119874

(4) for each point 119900119895in 119874119894

(5) compute begin time s time and end time e time of each event(6) if s time le 119905

119890ampamp e time ge 119905

119904

(7) push it into 119876119890 valid event

(8) handle events(9) time = 119905

119904 119871119901= 119871119904

(10) while (time le 119905119890)

(11) while (119876119890= NULL)

(12) 119890 = 119876119890sdot erase() pop queuersquos head

(13) while (119890 sdot 119905begin le time)(14) 119876handle sdot push back(119890) push 119890 into queue(15) 119890 = 119876

119890sdot erase()

(16) handle(119876handle) update 119876119890 and 119878119901(17) time++

Algorithm 2 PSUR algorithm

all time cost in initialization is119874(119889sdot119899(119899minus1)2+(Lenℎ)2(119899minus1) + 119899)

In second step the worst cost of comparison for staticdominant relationship between objects is 119874(119899(119899 minus 1)2) Theinteraction time for arbitrary two moving objectsrsquo distancefunction will cost119874(120575

1) where 120575

1is constantThus it will cost

119874(1205751sdot 119899(119899 minus 1)2) in this period

Handling events generates at most 119899(119899 minus 1)2 In theworst case each event is valid in time period [119905

119904 119905119890] and

this requires (119905119890minus 119905119904) times to deal with events In every

processing skyline probability related to trigger events willcost 119874((Lenℎ)2(119899 minus 1)) while update computing for eventis 119874(120575

2) where 120575

2is constant The total cost in this period is

119874((Lenℎ)2(119899minus1)sdot(119905119890minus119905119904) sdot119899(119899minus1)2+120575

2sdot (119905119890minus119905119904) sdot119899(119899minus1)2)

In conclusion the total cost is added together for thesethree periods which is equivalent to 119874(1198992)

6 Experimental Evaluation

61 Datasets Two real road networks are used to test theeffect and efficiency of the proposed algorithm PSUR Oneis the famous seashore city Oldenburg in Germany whichincludes 6105 nodes and 7036 edges The other is Cixi city ofChina which contains 244 intersection nodes and 407 edgesmuch smaller than the first oneWe assume that the uncertainarea is segment along the road Two distributions of uniformand Gaussian distribution for probability density functionare adopted because these two functions are by far the mostimportant and commonly used in statistics Moving objectsare generated randomly Baseline and priority algorithmsproposed in [8] are used to compare with our method PSURto verify efficiency and effect The main parameters aresegment length Len static dimension number 119889 numbers of

International Journal of Distributed Sensor Networks 7

50 5000

2

4

6

8

10

12

14

N

times104

100 200 300 400

Runt

ime (

ms)

(a) Gaussian distribution

50 100 200 300 400 5000

2

4

6

8

10

12

Runt

ime (

ms)

PriorityBaseline

PSUR

N

times104

(b) Uniform distribution

Figure 5 Numbers of moving objects effects of the performance inCixi city (119889 = 5 Len = 10 and 119905 = 20)

moving objects Num and time interval 119905 and probabilisticthreshold 119901 is 05 in all experiments

We conducted our experiments on desktop PC runningon Windows XP professional The PC has Intel Core 2Duo293GHz and 3GB RAM memory All experiments werecoded in Visual C++ 2008

62 Numbers of Moving Objects In this experiment suppose119889 = 5 Len = 10 and 119905 = 20 Figure 5 shows performanceof PSUR versus baseline and priority [8] when numbersof moving objects vary on Cixirsquos road network both in

Table 2 Event size in Cixi road network (119889 = 5 Len = 10 119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 669 35

100 2721 95

200 10389 205

300 35009 400

400 62723 514

500 96890 736

Table 3 Event size in Oldenburg road network (119889 = 5 Len = 10119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 245 5

100 455 15

200 1557 41

300 3945 131

400 6464 236

500 9951 367

uniform distribution and Gaussian distribution LikewiseFigure 10 demonstrates the performance on road networkin Oldenburg The figures show that runtime increases withobjectrsquos numbers whichever the model is No matter whatmodel is used uniform or Gaussian the cost in the samedataset is similar Among these three methods the responsetime of our algorithm is only one-tenth of the other twomethods It is because baseline and priority need recomputethe probabilistic skyline set at each time while PSUR is anincremental method

If there is the same number of moving objects in tworeal networks the density of moving objects in Cixi isbigger than that in Oldenburg because Cixi is smaller thanOldenburg Therefore the chances for interaction of movingobjects in Cixi are more those that in Oldenburg Triggerevents generated in Cixi are evidently more than those inOldenburg as Tables 2 and 3 show The density of movingobjects leads to this difference because it is more sparselydistributed in Oldenburg than in Cixi for the same numberof objects As a result by observing the performance betweentwo city networks under the same data model such asFigures 5(a) and 6(a) it is noted that the runtime in thesmaller city Cixi costs a little more than that in Oldenburg

The pruning strategy has done effective work on eventsize as Tables 2 and 3 show Event size will grow withthe number of moving objects because the number of theintersection of distance function rises

63 The Effect of Uncertain Segment Length In this sectionparameters are as follows Num = 50 119889 = 5 and 119905 = 20Figures 7 and 8 show performance of three algorithms whensegment length of uncertainty varies on Cixi road network

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 International Journal of Distributed Sensor Networks

Input one query object 119899moving objectsOutput Initialization 119901-skyline(1) 119878static = NULL(2) for any point 119900

119894in 119874

(3) compute path(119900119894) get the moving path of objects

(4) compute distance(119900119894) computing distance function

(5) 119874119894= NULL

(6) for any point 119900119895(119895 = 119894) in 119874

(7) compare(119900119878119895 119900119878119894) ensure whether 119874

119895dominate 119874

119894in static attributes

(8) if 119900119878119895≺ 119900119878

119894

(9) flag(119900119895 119900119894) = 1

(10) push 119900119895into the 119874

119894

(11) else(12) flag(119900

119895 119900119894) = 0

(13) if the 119874119894= NULL

(14) 119878static = 119878static cup 119900119894

Algorithm 1 Initialization

Input the set of moving objects119863 query point 119902 119901 is the probabilistic threshold the time interval [119905119904 119905119890]

Output the 119901-Skyline at any time instant 119905 within [119905119904 119905119890]

(1) initialization()(2) compute events(3) for any point 119900

119894in 119874

(4) for each point 119900119895in 119874119894

(5) compute begin time s time and end time e time of each event(6) if s time le 119905

119890ampamp e time ge 119905

119904

(7) push it into 119876119890 valid event

(8) handle events(9) time = 119905

119904 119871119901= 119871119904

(10) while (time le 119905119890)

(11) while (119876119890= NULL)

(12) 119890 = 119876119890sdot erase() pop queuersquos head

(13) while (119890 sdot 119905begin le time)(14) 119876handle sdot push back(119890) push 119890 into queue(15) 119890 = 119876

119890sdot erase()

(16) handle(119876handle) update 119876119890 and 119878119901(17) time++

Algorithm 2 PSUR algorithm

all time cost in initialization is119874(119889sdot119899(119899minus1)2+(Lenℎ)2(119899minus1) + 119899)

In second step the worst cost of comparison for staticdominant relationship between objects is 119874(119899(119899 minus 1)2) Theinteraction time for arbitrary two moving objectsrsquo distancefunction will cost119874(120575

1) where 120575

1is constantThus it will cost

119874(1205751sdot 119899(119899 minus 1)2) in this period

Handling events generates at most 119899(119899 minus 1)2 In theworst case each event is valid in time period [119905

119904 119905119890] and

this requires (119905119890minus 119905119904) times to deal with events In every

processing skyline probability related to trigger events willcost 119874((Lenℎ)2(119899 minus 1)) while update computing for eventis 119874(120575

2) where 120575

2is constant The total cost in this period is

119874((Lenℎ)2(119899minus1)sdot(119905119890minus119905119904) sdot119899(119899minus1)2+120575

2sdot (119905119890minus119905119904) sdot119899(119899minus1)2)

In conclusion the total cost is added together for thesethree periods which is equivalent to 119874(1198992)

6 Experimental Evaluation

61 Datasets Two real road networks are used to test theeffect and efficiency of the proposed algorithm PSUR Oneis the famous seashore city Oldenburg in Germany whichincludes 6105 nodes and 7036 edges The other is Cixi city ofChina which contains 244 intersection nodes and 407 edgesmuch smaller than the first oneWe assume that the uncertainarea is segment along the road Two distributions of uniformand Gaussian distribution for probability density functionare adopted because these two functions are by far the mostimportant and commonly used in statistics Moving objectsare generated randomly Baseline and priority algorithmsproposed in [8] are used to compare with our method PSURto verify efficiency and effect The main parameters aresegment length Len static dimension number 119889 numbers of

International Journal of Distributed Sensor Networks 7

50 5000

2

4

6

8

10

12

14

N

times104

100 200 300 400

Runt

ime (

ms)

(a) Gaussian distribution

50 100 200 300 400 5000

2

4

6

8

10

12

Runt

ime (

ms)

PriorityBaseline

PSUR

N

times104

(b) Uniform distribution

Figure 5 Numbers of moving objects effects of the performance inCixi city (119889 = 5 Len = 10 and 119905 = 20)

moving objects Num and time interval 119905 and probabilisticthreshold 119901 is 05 in all experiments

We conducted our experiments on desktop PC runningon Windows XP professional The PC has Intel Core 2Duo293GHz and 3GB RAM memory All experiments werecoded in Visual C++ 2008

62 Numbers of Moving Objects In this experiment suppose119889 = 5 Len = 10 and 119905 = 20 Figure 5 shows performanceof PSUR versus baseline and priority [8] when numbersof moving objects vary on Cixirsquos road network both in

Table 2 Event size in Cixi road network (119889 = 5 Len = 10 119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 669 35

100 2721 95

200 10389 205

300 35009 400

400 62723 514

500 96890 736

Table 3 Event size in Oldenburg road network (119889 = 5 Len = 10119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 245 5

100 455 15

200 1557 41

300 3945 131

400 6464 236

500 9951 367

uniform distribution and Gaussian distribution LikewiseFigure 10 demonstrates the performance on road networkin Oldenburg The figures show that runtime increases withobjectrsquos numbers whichever the model is No matter whatmodel is used uniform or Gaussian the cost in the samedataset is similar Among these three methods the responsetime of our algorithm is only one-tenth of the other twomethods It is because baseline and priority need recomputethe probabilistic skyline set at each time while PSUR is anincremental method

If there is the same number of moving objects in tworeal networks the density of moving objects in Cixi isbigger than that in Oldenburg because Cixi is smaller thanOldenburg Therefore the chances for interaction of movingobjects in Cixi are more those that in Oldenburg Triggerevents generated in Cixi are evidently more than those inOldenburg as Tables 2 and 3 show The density of movingobjects leads to this difference because it is more sparselydistributed in Oldenburg than in Cixi for the same numberof objects As a result by observing the performance betweentwo city networks under the same data model such asFigures 5(a) and 6(a) it is noted that the runtime in thesmaller city Cixi costs a little more than that in Oldenburg

The pruning strategy has done effective work on eventsize as Tables 2 and 3 show Event size will grow withthe number of moving objects because the number of theintersection of distance function rises

63 The Effect of Uncertain Segment Length In this sectionparameters are as follows Num = 50 119889 = 5 and 119905 = 20Figures 7 and 8 show performance of three algorithms whensegment length of uncertainty varies on Cixi road network

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 7

50 5000

2

4

6

8

10

12

14

N

times104

100 200 300 400

Runt

ime (

ms)

(a) Gaussian distribution

50 100 200 300 400 5000

2

4

6

8

10

12

Runt

ime (

ms)

PriorityBaseline

PSUR

N

times104

(b) Uniform distribution

Figure 5 Numbers of moving objects effects of the performance inCixi city (119889 = 5 Len = 10 and 119905 = 20)

moving objects Num and time interval 119905 and probabilisticthreshold 119901 is 05 in all experiments

We conducted our experiments on desktop PC runningon Windows XP professional The PC has Intel Core 2Duo293GHz and 3GB RAM memory All experiments werecoded in Visual C++ 2008

62 Numbers of Moving Objects In this experiment suppose119889 = 5 Len = 10 and 119905 = 20 Figure 5 shows performanceof PSUR versus baseline and priority [8] when numbersof moving objects vary on Cixirsquos road network both in

Table 2 Event size in Cixi road network (119889 = 5 Len = 10 119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 669 35

100 2721 95

200 10389 205

300 35009 400

400 62723 514

500 96890 736

Table 3 Event size in Oldenburg road network (119889 = 5 Len = 10119905 = 20)

Numbers of movingobjects

Event size beforepruning

Event size afterpruning

50 245 5

100 455 15

200 1557 41

300 3945 131

400 6464 236

500 9951 367

uniform distribution and Gaussian distribution LikewiseFigure 10 demonstrates the performance on road networkin Oldenburg The figures show that runtime increases withobjectrsquos numbers whichever the model is No matter whatmodel is used uniform or Gaussian the cost in the samedataset is similar Among these three methods the responsetime of our algorithm is only one-tenth of the other twomethods It is because baseline and priority need recomputethe probabilistic skyline set at each time while PSUR is anincremental method

If there is the same number of moving objects in tworeal networks the density of moving objects in Cixi isbigger than that in Oldenburg because Cixi is smaller thanOldenburg Therefore the chances for interaction of movingobjects in Cixi are more those that in Oldenburg Triggerevents generated in Cixi are evidently more than those inOldenburg as Tables 2 and 3 show The density of movingobjects leads to this difference because it is more sparselydistributed in Oldenburg than in Cixi for the same numberof objects As a result by observing the performance betweentwo city networks under the same data model such asFigures 5(a) and 6(a) it is noted that the runtime in thesmaller city Cixi costs a little more than that in Oldenburg

The pruning strategy has done effective work on eventsize as Tables 2 and 3 show Event size will grow withthe number of moving objects because the number of theintersection of distance function rises

63 The Effect of Uncertain Segment Length In this sectionparameters are as follows Num = 50 119889 = 5 and 119905 = 20Figures 7 and 8 show performance of three algorithms whensegment length of uncertainty varies on Cixi road network

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 International Journal of Distributed Sensor Networks

50 5000

2

4

6

8

10

12

14

N

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

500

2

4

6

8

10

N

12times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 6 Numbers of moving objects effect of the performance in Oldenburg city (119889 = 5 Len = 10 and 119905 = 20)

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 10 20 40 600

1

2

3

4

5

6

7

8

9

10

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 7 Segment length effects of the performance in Cixi city (Num = 50 119889 = 5 119905 = 20)

andOldenburg city respectively both in uniformdistributionand Gaussian distribution

Themagnitude of the uncertain lengthmay also affect theperformance of algorithm PSUR It is seen that the longerthe segment length is the more runtime is required If thelength becomes much longer for any two objects 119874

119894and 119874

119895

the probability that Pr(119874119895≺ 119874119894) = 0 Pr(119874

119895≺ 119874119894) = 1 happen

becomes greater According to the definition of event the sizeof event queue will increase so will the times to track andhandle events The calculation of dominance probability and

skyline probability grows with this increasing probability sothat the cost will go up

It is shown that the segment length of uncertainty affectseventrsquos size as shown in Tables 4 and 5 With increase ofsegment length the number of events becomes great

64 The Effect of Static Attribute Dimensionality We willdiscuss the effect that multidimensional attributes impact onour algorithm over real road network The result is shownin Figures 9 and 10 It is known that the higher dimension

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 9

2 10 20 40 600

2

4

6

8

10

12

14

L

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 10 20 40 600

2

4

6

8

10

12

L

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 8 Segment length effects of the performance in Oldenburg city (Num = 50 119889 = 5 119905 = 20)

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 9 Static attribute dimensionality effects of the performance in Cixi city (Num = 50 Len = 20 119905 = 20)

results in less run-time This is because the computation ofdominance relation on static attributes is carried out onlyonce at the beginning The higher the static dimensions arethe less objects that dominant 119900

119894areThe less the time cost on

computation of initializing adjacency list and event queue isthe less the total runtime is

Tables 6 and 7 show the event size changes with staticdimensionality of PSUR Unlike preceding two experimentsin this case when static dimensionality 119889 increases the event

size reduces instead of increasing This is due to the fact thatwhen 119889 increases the number of moving objects which havedominant relationship in static dimensionality decreasesThedistance function will interact less so will valid events

65 The Effect of Time Span Baseline and priority aresomewhat static algorithms They need to recompute skylineprobability for each moving object so runtime is propor-tional to the time spanHowever as a dynamicmethod PSUR

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 International Journal of Distributed Sensor Networks

2 3 4 5 6 70

1

2

3

4

d

times104Ru

ntim

e (m

s)

(a) Gaussian distribution

2 3 4 5 6 70

1

2

3

4

d

times104

Runt

ime (

ms)

(b) Uniform distribution

Figure 10 Static attribute dimensionality effects of the performance in Oldenburg city (Num = 50 Len = 20 119905 = 20)

5 10 20 50 800

1

2

3

4

t

times105

Runt

ime (

ms)

(a) Gaussian distribution

5 10 20 50 80 1000

1

2

3

4

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 11 Time span effects of the performance in Cixi city (119889 = 5 Len = 20 Num = 100)

can update the 119901-skyline set by tracking event size to decidewhich one might vary so the time cost is approximately thesame as in each timestamp which savesmore time than othertwo algorithms Figures 11 and 12 show this evidence

Tables 8 and 9 show the event size changes with time spanlength of PSUR It is obvious that the event size grows withincreasing time span length Nevertheless the difference isnot significant The runtime of PSUR varies a little in Figures11 and 12

7 Conclusion

To the best of our knowledge this is the first work tocompute probabilistic skyline queries for uncertainty in roadnetwork In this paper we have addressed the problem ofcontinuous probabilistic skyline query for moving objectsFirstly attributes of objects are divided into static anddynamic to define dominant probability and skyline proba-bility with continuous data In order to update the skyline

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 11

5 10 20 50 80 1000

1

2

t

times105Ru

ntim

e (m

s)

(a) Gaussian distribution

5 10 20 50 800

1

2

t

times105

Runt

ime (

ms)

(b) Uniform distribution

Figure 12 Time span effects of the performance in Oldenburg city (119889 = 5 Len = 20 Num = 100)

Table 4 Event size in Cixi road work (119889 = 5 Num = 50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 1029 3910 1597 5120 2264 8240 3387 11360 4147 137100 4450 144

Table 5 Event size in Oldenburg road work (119889 = 5 Num = 50119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 190 210 245 520 306 640 461 760 611 7100 890 16

set continuously trigger events are introduced to computevarying skyline probability of objects Two pruning ways areproposed to save search space and speed up this computationAt last the continuous probabilistic skyline query algorithmwith uncertainty in road network named PSUR is proposedFinally a series of experiments are devised to verify theeffectiveness and efficiency of PSUR The results of our

Table 6 Event size in Cixi road network (Len = 20 Num = 50119905 = 20)

Staticdimensionality 119889

Event size beforepruning

Event size afterpruning

2 543 97

3 558 72

4 665 37

5 519 21

6 620 10

7 625 5

Table 7 Event size in Oldenburg road network (Len = 20 Num =50 119905 = 20)

Segment length Event size beforepruning

Event size afterpruning

2 101 4110 118 1420 121 740 124 660 128 4100 122 2

experimental study for different scales of datasets on tworeal road networks are very encouraging The investigationdemonstrates that the proposed updating method is moreeffective and efficient than periodic methods

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 International Journal of Distributed Sensor Networks

Table 8 Event size in Cixi road network (Len = 20 Num = 100119889 = 5)

Time span length Event size beforepruning

Event size afterpruning

5 1029 3910 1597 5120 2264 8250 3387 11380 4147 137100 4450 144

Table 9 Event size in Oldenburg road network (Len = 20 Num =100 119889 = 5)

Segment length Event size beforepruning

Event size afterpruning

5 359 910 481 1320 583 1550 714 2080 830 24100 914 28

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research is partly supported by the Zhejiang NaturalScience Foundation (LY12F02020) Ningbo Natural ScienceFoundation (2013A610063 2012A610066) and the K CWong Magna Fund in Ningbo University

References

[1] O Wolfson A P Sistla S Chamberlain and Y Yesha ldquoUpdat-ing and querying databases that trackmobile unitsrdquoDistributedand Parallel Databases vol 7 no 3 pp 257ndash287 1999

[2] G S Iwerks H Samet and K Smith ldquoContinuous k-nearestneighbor queries for continuouslymoving points with updatesrdquoin Proceedings of the International Conference on Very LargeData Bases (VLDB rsquo03) pp 512ndash523 2003

[3] H Mokhtar J Su and O Ibarra ldquoOn moving object queriesrdquoin Proceedings of the 21st ACM SIGMOD-SIGACT-SIGARTSymposium on Principles of Database Systems (PODS rsquo02) pp188ndash198 June 2002

[4] Z Huang H Lu B C Ooi and A K H Tung ldquoContinuousskyline queries for moving objectsrdquo IEEE Transactions onKnowledge and Data Engineering vol 18 no 12 pp 1645ndash16582006

[5] R Cheng D V Kalashnikov and S Prabhakar ldquoQueryingimprecise data in moving object environmentsrdquo IEEE Transac-tions on Knowledge andData Engineering vol 16 no 9 pp 1112ndash1127 2004

[6] D Pfoser and C Jensen ldquoCapturing the uncertainty of moving-objects representationsrdquo in Proceedings of International Confer-ence on Scientific and Statistical DatabaseManagement vol 1651of Lecture Notes in Computer Science pp 111ndash131 1999

[7] X Ding and Y Lu ldquoIndexing the imprecise positions of movingobjectsrdquo inProceedings of theACMSIGMODPhDWorkshop onInnovative Database Research pp 45ndash50 Beijing China 2007

[8] C Bohm F Fiedler A Oswald C Plant and BWackersreutherldquoProbabilistic skyline queriesrdquo in Proceedings of the 18th ACMInternational Conference on Information and Knowledge Man-agement (CIKM rsquo09) pp 651ndash660 HongKong November 2009

[9] S Borzsony D Kossmann and K Stocker ldquoThe skyline opera-torrdquo in Proceedings of the 17th International Conference on DataEngineering pp 421ndash430 Heidelberg Germany April 2001

[10] J Chomicki P Godfrey and J Gryz ldquoSkyline with presortingtheory and optimizationrdquo in Proceedings of the 14th Interna-tional Conference on Intelligent Information System pp 593ndash6022005

[11] D Kossmann F Ramsak and S Rost ldquoShooting stars in the skyan online algorithm for skyline queriesrdquo in Proceedings of theInternational Conference on Very Large Data Bases (VLDB rsquo02)pp 275ndash286 Hong Kong 2002

[12] D Papadias Y Tao G Fu and B Seeger ldquoProgressive sky-line computation in database systemsrdquo ACM Transactions onDatabase Systems vol 30 no 1 pp 41ndash82 2005

[13] Y Tao and D Papadias ldquoMaintaining sliding window skylineson data streamsrdquo IEEE Transactions on Knowledge and DataEngineering vol 18 no 3 pp 377ndash391 2006

[14] L Tian P Zou A-P Li and Y Jia ldquoGrid index based algorithmfor continuous skyline computationrdquo Chinese Journal of Com-puters vol 31 no 6 pp 998ndash1012 2008

[15] M Kontaki A N Papadopoulos and Y Manolopoulos ldquoCon-tinuous k-dominant skyline computation on multidimensionaldata streamsrdquo in Proceedings of the 23rd Annual ACM Sym-posium on Applied Computing (SAC rsquo08) pp 956ndash960 March2008

[16] Y Ishikawa Y Iijima and J X Yu ldquoSpatial range querying forGaussian-based imprecise query objectsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 676ndash687 April 2009

[17] F Fiedler Probabilistic skyline queries on uncertain data [Ph Ddissertation] 2006

[18] J Pei B Jiang X Lin et al ldquoProbabilistic skylines on uncertaindatardquo in Proceedings of the 33th International Conference onVeryLarge Databases(VLDB rsquo07) pp 253ndash264 Vienna Austria 2007

[19] X Lian and L Chen ldquoMonochromatic and bichromatlc reverseskyline search over uncertain databasesrdquo in Proceedings of theACM SIGMOD International Conference on Management ofData (SIGMOD rsquo08) pp 213ndash226 June 2008

[20] WZhang X Lin Y ZhangWWang and J X Yu ldquoProbabilisticskyline operator over sliding windowsrdquo in Proceedings of the25th IEEE International Conference on Data Engineering (ICDErsquo09) pp 1060ndash1071 April 2009

[21] M J Atallah and Y Qi ldquoComputing all skyline probabilitiesfor uncertain datardquo in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems(PODS rsquo09) pp 279ndash287 July 2009

[22] X Ding X Lian L Chen and H Jin ldquoContinuous monitoringof skylines over uncertain data streamsrdquo Information Sciencesvol 184 no 1 pp 196ndash214 2012

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of Distributed Sensor Networks 13

[23] X Lin J Xu and H Hu ldquoRange-based skyline queries inmobile environmentsrdquo IEEE Transactions on Knowledge andData Engineering vol 25 no 4 pp 835ndash849 2013

[24] X Huang and C S Jensen ldquoIn-route skyline querying forlocation-based servicesrdquo in Proceedings of the 4th InternationalWorkshop on Web and Wireless Geographical Information Sys-tems (W2GIS rsquo04) vol 3428 of Lecture Notes in ComputerScience pp 120ndash135 November 2004

[25] K Deng X Zhou and H T Shen ldquoMulti-source skylinequery processing in road networksrdquo in Proceedings of the 23rdInternational Conference on Data Engineering (ICDE rsquo07) pp796ndash805 April 2007

[26] S M Jang and J S Yoo ldquoProcessing continuous skylinequeries in road networksrdquo in Proceedings of the InternationalSymposium on Computer Science and Its Applications (CSA rsquo08)pp 353ndash356 October 2008

[27] H-P KriegelM Renz andM Schubert ldquoRoute skyline queriesa multi-preference path planning approachrdquo in Proceedings ofthe 26th IEEE International Conference on Data Engineering(ICDE rsquo10) pp 261ndash272 March 2010

[28] W Lee C S-H Eom and T-C Jo ldquoPath skyline for movingobjectsrdquoWeb Technologies and Applications Springer vol 7235pp 610ndash617 2012

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of