multiprocessing and scalability · 17. broadcasting indexing objects on air channel. advantages....
TRANSCRIPT
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Mobile and Heterogeneous databases Broadcasting
A.R. HursonComputer Science
Missouri Science & Technology
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Note, this unit will be covered in ninelectures. In case you finish it earlier, thenyou have the following options:
1) Take the early test and start CS6302.module102) Study the supplement module
(supplement CS6302.module9)3) Act as a helper to help other students in
studying CS6302.module9Note, options 2 and 3 have extra credits as noted in courseoutline.
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Broadcasting
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Glossary of prerequisite topics
Familiar with the topics?No Review
CS6302.module9.background
Yes
Remedial actionYes
NoTake the Module
Take Test
Pass?
Glossary of topics
Familiar with the topics?Yes
Pass?
Take Test
Yes
Options
Lead a group of students in this module (extra credits)?
Study more advanced related topics (extra credits)?
Study next module?
No
{
Extra Curricular activities
Enforcement of background
{Current ModuleAt the end give a
test, record the score, and impose remedial
action if not successful
No
Broadcasting
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You are expected to be familiar with: Mobile DataAccess Systems, if not, you need to
study CS6302.module7.
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Wireless Communication & Mobility
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Previous module introduced mobility and wirelesscommunication in traditional multidatabase platform.As you recall, we distinguished three classes of data andthree classes of services.
This module will concentrate on “public data” and“broadcasting” as a means to make public data availableto the users.
Within the scope of broadcasting, we will talk aboutchallenges and potential solutions.
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Broadcasting
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Broadcasting
Many applications are directed towardspublic information that are characterized bythe: Massive number of users, Similarity and simplicity in the requests, and Fact that data is modified by a few (at the
server level).
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Broadcasting
The reduced bandwidth attributed to thewireless environment places limitationson the rate and amount ofcommunication.
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Broadcasting
Broadcast-Based Service In such an environment, broadcasting has
been suggested as a possible solution forquery processing. In broadcasting, public data is broadcast over the
air channel. A mobile host unit, in search of data, could tune
to the appropriate frequency upon which the datais being broadcast.
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Broadcasting
Broadcast-Based Service Lower Bandwidth: Response time is independent of
the number of users accessing a channel — it scales upas the number of users increases.
Limited Energy Resources: Less energy is consumedto receive (to pull) an information from the air channelthan sending (to push) the information.
Limited Storage Medium: Air channel can beconsidered as a persistent storage medium.
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Broadcasting
Broadcast-Based Service ─ Challenges Power Consumption ─ Application of index and
organization of objects on broadcast channel (s). Network Latency ─ Application of parallel channels to
reduce broadcast length: Distribution of Objects over parallel channels, Creation of Conflicts.
Broadcasting contents ─ Application specific domain.
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Broadcast-Based Service Application of Index in Single and Parallel
Broadcast Channel(s), Data Organization on Single and Parallel
Broadcast Channel(s), Heuristic and Theoretical conflict resolution
schemes, Conflict resolution in the face of replication.
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Broadcasting
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Broadcasting
Retrieving information from the air channelhas two requirements: Minimizing the overall response time at the
mobile unit, and Minimizing the amount of power consumed in
the retrieval process at the mobile unit.
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Broadcasting
Indexing Objects on air Channel An index is a mechanism that speeds up associative
searching. It has been extensively used in traditionalfile and database systems.
An index can be formally defined as a function thattakes a key value and provides an address referring tothe location of the associated data. Its main advantagelies in the fact that it eliminates the need for anexhaustive search through the pages of the data on thestorage medium.
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Broadcasting
Indexing Objects on air Channel B-trees, B+-trees, and hash tables are some of
the most common data structures that havebeen used to implement indexes.
In databases, an index is used during the queryoptimization stage as part of query processing.Normally, a query engine generates multipleplans that can be used to access the requireddata.
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Broadcasting
Indexing Objects on air Channel Similarly, within the scope of broadcasting, an index is
an auxiliary information pointing to the location orpossible availability of a data item on the broadcast andhence, allowing mobile unit to predict the arrival timeof the data item requested.
The prediction of the arrival time enables the mobileunit to switch its operational mode into an energy-saving mode.
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Broadcasting
Indexing Objects on air Channel In short, an indexing mechanism facilitates
object retrieval from the air channel(s),reducing power consumption.
It should be noted that the advantages ofindexing schemes come at the expense ofcomputational overhead and increased lengthof the broadcast (response time).
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Broadcasting
Indexing Objects on air Channel
Advantages Disadvantages
Provides auxiliary information that allows mobile users to predict arrival time of objects.
Longer Broadcast.
Enables utilization of different operational modes (active, nap, doze, etc).
Longer response time.
Reduces power consumption (less tune-in time). Computational overhead due to complexity in retrieval, allocation,and maintenance of the indexes.
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Broadcasting
Indexing Objects on air Channel ─ Signature-BasedIndexing A signature is an abstraction of the information stored
in a record or a file. The basic idea behind the application and use of
signatures in a broadcast channel is to add a controlpart to the contents of an information frame.
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Broadcasting
Indexing Objects on air Channel ─ Signature-Based Indexing A hash function is applied to the contents of the information
frame, generating a bit vector and superimposing it on the dataframe.
A signature partially reflects the data content of a frame. Inshort, this technique creates a set of signatures for data frameson a broadcast and interleaves them with their associated dataframe.
Different allocation schemes of signatures on a broadcastchannel have been studied in the literature; Single signature, Integrated signature and Multi-level signature.
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Broadcasting
Indexing Objects on air Channel ─ Signature-Based Indexing In the single signature scheme, the signature frame is
broadcast before the corresponding data frame. In the integrated signature scheme, a signature is
constructed for a group of consecutive frames calleda frame group.
The multi-level signature scheme is a combination ofthe single and integrated signature methods in whichthe upper level signatures are integrated signaturesand the lower level signatures are single signatures.
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Broadcasting
Indexing Objects on air Channel ─ Signature-BasedIndexing During the retrieval process, a query is resolved by generating
a signature based on the user’s request. The query signature is then compared against the signatures of
the data frames in the broadcast. A successful match indicates a possible hit. Consequently, the
content of the corresponding information frame is checkedagainst the query to verify that it corresponds to the user’sdemands.
If the data of the frame corresponds to the user’s request, thedata is recovered; otherwise, the corresponding informationframe is ignored.
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Broadcasting
Indexing Objects on air Channel ─ Signature-Based Indexing In general, the signature based scheme reduces the
access time and the tune-in time when pullinginformation from the air channel.
By checking the signature, the mobile unit partiallydetermines the validity of the content of aninformation frame ─ if the data frame does notcorrespond to the query, the mobile unit switchesfrom active mode to doze mode and waits until thenext signature is transmitted.
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Broadcasting
Indexing Objects on air Channel ─ Signature-BasedIndexing As part of the studies done on signature-based indexing
schemes, the three aforementioned signature-based schemeshave been analyzed with respect to each other using the accesstime and tune-in time as the performance metrics: With fixed signature size, the multi-level scheme has the best
tune-in time performance at the expense of a longer access time. The integrated scheme, on the other hand, has the best average
access time, but its tune-in time depends on the similarity amongthe information frames.
Finally, the simple scheme has an adequate access time and tune-in time.
In general, in comparison to broadcasting without using indexing,all three signature-based schemes improved tune-in timeperformance significantly with a reasonable access timeoverhead.
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Broadcasting
Indexing Objects on air Channel ─ Tree-Based Indexing As noted before, an index is auxiliary information representing
one or several data attributes pointing to the location of datacollection (i.e., information frames) sharing the same commonattribute value(s).
This auxiliary information is usually organized as a tree inwhich the lowest level of the tree points to the location of theinformation frames on the broadcast channel.
With this concept in mind, the frames on the broadcast are oftwo kinds: Data frames and Index frames.
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Broadcasting
Indexing Objects on air Channel ─ Tree-BasedIndexing A broadcast channel is a sequential medium and
hence, to reduce the mobile unit active and tune-intime, and consequently to reduce the powerconsumption, the index frames are usually replicatedand interleaved with the data frames. Otherwise, therequest would have to wait for the beginning of thenext broadcast cycle an increase in the queryresponse time.
One study investigated two index replicationschemes: Distributed indexing and (1, m) indexing
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Broadcasting
Indexing Objects on air Channel ─ Tree-BasedIndexing In distributed indexing, the index is partitioned and
interleaved in the broadcast cycle. Each part of theindex in the broadcast is followed by itscorresponding data frame(s).
In (1, m) indexing, the entire index is interleaved mtimes during the broadcast cycle the whole indexis broadcast before every 1/m fraction of the cycle.
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Broadcasting
Indexing Objects on air Channel ─ Tree-BasedIndexing A series of analysis for both methods were carried
out and compared with the algorithms that providedthe best case for tune-in time and response time.
It was concluded that, in general, the (1, m) indexingscheme reduces power consumption at the expenseof an increase in the response time.
The distributed indexing scheme, relative to the (1,m) indexing scheme, increases the response time at amuch lower rate at the expense of higher powerconsumption.
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Broadcasting
Indexing Objects on air Channel ─ Tree-Based Indexing Previous work has shown that the tree-based indexing schemes
are more suitable for the application domains where informationis accessed from the broadcast channel randomly, and thesignature-based indexing schemes are more suitable in retrievingsequentially structured data elements.
In addition, tree-based indexing schemes have shown superiorityover the signature-based indexing schemes when user request isdirected towards interrelated objects clustered on the broadcastchannel(s). Furthermore, tree-based indexing schemes relative tosignature-based indexing schemes are more suitable in reducingthe overall power consumption.
A tree-based indexing provides global information regarding thephysical location of the data frames on the broadcast channel. Onthe other hand, signature-based indexing schemes are moreeffective in retrieving data frames based on multiple attributes.
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Broadcasting
Indexing Objects on air Channel
Feature Signature -based Indexing
Tree -based Indexing
Less power consumption √
Longer length of broadcast √ √
Computational overhead √ √
Longer response time √ √
Shorter tune-in time √
Random data access √
Sequentially structured data √
Clustered data retrieval √
Multi-attribute retrieval √
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing In general, in the presence of an indexing mechanism
one can adapt the following protocol for retrieving dataobjects from the air channel(s) in order to minimize thepower consumption.
The protocol involves the following steps: Initial probe: The client tunes into the broadcast channel to
determine when the next index tree is broadcast. Search: The client accesses the index and determines the offset
for the requested objects. Retrieve: The client tunes into the channel and downloads all
the required data objects.
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Broadcasting
Indexing Objects on air Channel ─ Object Oriented Indexing Object-oriented indexing is normally implemented via a multi-
level tree. We can classify the possible implementation techniques into two
general schemes: Single-class indexing and Hierarchical indexing.
In the single-class scheme, multiple multi-level trees areconstructed, each representing one class. In this case, the leafnodes of each tree point to objects belonging only to the classindexed by that tree.
The hierarchical-based scheme constructs one multi-level treerepresenting an index for all classes. The same query has to onlynavigate the common tree.
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Broadcasting
Indexing Objects on air Channel ─ ObjectOriented Indexing
Single-Class-Based IndexTrees
… …
:.
… …
…
…
Objects From a Single Class
:.
:.
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Broadcasting
Indexing Objects on air Channel ─ ObjectOriented Indexing
… … …Inner Nodes
… … … …
Data …
Hierarchical-Based Index Trees
Objects From Multiple Classes
Leaf Nodes :.:.:.
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing We assume an air-channel page as the storage granule on the air
channel. Due to the sequential nature of the air channel, the allocation of the
nodes of a multi-level tree has to follow the navigational path usedto traverse the tree, starting at the root. Therefore, an orderingscheme is used to sequentially map the nodes on the air channel.Similarly, data objects are allocated onto air channel pagesfollowing their index.
Note that, it is possible to interleave and distribute the index pagesand associated data pages in a variety of methods.
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing
Previous D n I1
In Dn
Single Class Scheme
I3
I2
…
D 2D 1
D3 Next I1
Previous D
Hierarchical Scheme
IH D Next I H
I i Index of single class iDiData of single class i
IH Hierarchical index
D Data of all classes
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing (Hierarchical Method) In this scheme, whether the domain of the query covers one class
or all classes along the hierarchy, the same index structure has tobe traversed.
Any request has to probe the channel first, read one page, and getan offset to the first page of the index.
The modules of the mobile unit can then go into doze mode. Oncethe index is reached the modules are brought back into activemode.
A number of index pages are read and offsets to the requiredobjects are obtained. The offsets are followed and the requiredobjects are retrieved. In the interim between the retrieval ofobjects, the modules are brought into doze mode.
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Broadcasting
Indexing Objects on air Channel ─ Object Oriented Indexing(Hierarchical Method)
Hierarchical ProtocolProbe onto channel and get offset to the next index activeReach the index dozeRetrieve the required index pages activeReach the required data pages dozeRetrieve required data pages active
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing (Single Class Method) Single-Class Protocol
Probe onto channel and get offset to the next index activeReach the index dozeRetrieve offsets to the indexes of required classes activefor every required class
Reach the index dozeRetrieve the required index pages activeReach the required data dozeRetrieve required data pages active
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Broadcast-Based Service ─ Simulation A simulator was developed to evaluate the feasibility and
effectiveness of the proposed algorithms. The NASDAQ database with 4290 securities is used as the source
data for the objects on the broadcast. The simulator views the parallel air channels as a two-dimensional
N × M array, where N and M represent the number of parallel airchannels and the number of objects on a broadcast, respectively.
For each simulation run, user requests are generated, randomly,requesting K objects on the broadcast.
For every simulated configuration, the simulator is run 1000 times,and the average number of every estimated performance metric iscalculated and reported.
Broadcasting
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing Response Time Degradation Relative to the No-
Indexing SchemeAggregation/Hierarchical
Aggregation/Single
Inheritance/Hierarchical
Inheritance/Single
1.17 1.05 1.1 1.02
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing Response Time vs. Number of Retrieved Classes
0
20
40
60
80
100
120
140
160
12.5 25 50 75 87.5 100
Percentage of Retrieved Classes
Res
pons
e T
ime
(Sec
.)
Aggr/SnglAggr/HierInher/SnglInher/Hier
Chart2
12.512.512.512.5
25252525
50505050
75757575
87.587.587.587.5
100100100100
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage of Retrieved Classes
Response Time (Sec.)
28.4765625
62.03125
67.5140625
139.8217447917
32.2265625
63.39296875
82.1
140.9602213542
40.0026041667
64.296875
93.3
142.206640625
47.2
66.2109375
110.4
145.1132161458
52.4674479167
67.0916294643
118.7
146.1540364583
56
67.3082589286
129.9
147.0432291667
PCRAS
Data Rate1048576bits/sec
Power Active0.13W
Power Doze0.0066W
Response TimeActive TimeEnergy
AggregationInheritanceAggregationInhertianceAggregationInheritance
In PagesIn SecIn PagesIn SecIn PagesIn mSecIn PagesIn mSecIn mJoules
PercentagePrcnt Cls RtrAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierInher/SnglInher/Hier
0.12512.57,29015,880286217,28435,794681401615615718206978196416454932
0.25258,25016,229326321,01836,086821413518138713828149109230427560944
0.55010,24116,460406423,88536,405931425723223896546254180291435647961
0.757512,08316,950476628,26237,14911014585323311248763338245352452770988
0.87587.513,43217,175526730,38737,41511914695373711459672377281392461830999
110014,33617,231566733,25437,64313014711140432157112814393164234649111,010
PCRAS
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
Seconds
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
m Seconds
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
m Joules
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42
Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing Active Time vs. Number of the Retrieved Classes
0
100
200
300
400
500
600
12.5 25 50 75 87.5 100
Percentage of Retrieved Classes
Act
ive
Tim
e (m
Sec
.)
Aggr/SnglAggr/HierInher/SnglInher/Hier
Chart9
12.512.512.512.5
25252525
50505050
75757575
87.587.587.587.5
100100100100
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage of Retrieved Classes
Active Time (m Sec.)
23.75
49.21875
37.65625
45
117.28515625
63.28125
144.62890625
98
190.75
80.859375
257.65625
156.25
263.75
115.9598214286
353
209
322
137.109375
435
257.8125
378
149.609375
500
292.96875
PCRAS
Data Rate1048576bits/sec
Power Active0.13W
Power Doze0.0066W
Response TimeActive TimeEnergy
AggregationInheritanceAggregationInhertianceAggregationInheritance
In PagesIn SecIn PagesIn SecIn PagesIn mSecIn PagesIn mSecIn mJoules
PercentagePrcnt Cls RtrAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierInher/SnglInher/Hier
0.12512.57,29015,880286217,28435,79468140613244910123845191415450928
0.25258,25016,229326321,01836,08682141301611763372514598227426560942
0.55010,24116,460406423,88536,405931424921191816640258156288434648958
0.757512,08316,950476628,26237,14911014568302641169054353209344451772984
0.87587.513,43217,175526730,38737,415119146823532213711166435258386460837996
110014,33617,231566733,25437,6431301479738378150128755002934164639191,007
PCRAS
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
Seconds
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
m Seconds
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
m Joules
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43
Broadcasting
Indexing Objects on air Channel ─ ObjectOriented Indexing Energy Improvement Relative to the No-Index
SchemeAggregation/Hierarchical
Aggregation/Single
Inheritance/Hierarchical
Inheritance/Single
17.5 18.9 18.4 19
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Broadcasting
Indexing Objects on air Channel ─ Object OrientedIndexing Detailed Energy Consumption
0
200
400
600
800
1,000
1,200
12.5 25 50 75 87.5 100
Percentage of Retrieved Classes
Ener
gy (m
Jou
les)
Aggr/SnglAggr/HierInher/SnglInher/Hier
Chart10
12.512.512.512.5
25252525
50505050
75757575
87.587.587.587.5
100100100100
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage of Retrieved Classes
Energy (m Joules)
190.8760625
415.47984375
450.23959375
928.376515625
227.1683007812
426.2025
559.7072070313
942.4306609375
287.5557375
434.337421875
647.57478125
957.845078125
344.06675
451.3016294643
772.2002
983.5378265625
386.01995625
459.7240513393
837.099
996.430703125
416.2452
462.6963058036
919.04
1006.63765625
PCRAS
Data Rate1048576bits/sec
Power Active0.13W
Power Doze0.0066W
Response TimeActive TimeEnergy
AggregationInheritanceAggregationInhertianceAggregationInheritance
In PagesIn SecIn PagesIn SecIn PagesIn mSecIn PagesIn mSecIn mJoules
PercentagePrcnt Cls RtrAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierAggr/SnglAggr/HierInher/SnglInher/HierInher/SnglInher/HierAggr/SnglAggr/HierInher/SnglInher/Hier
0.12512.57,29015,880286217,28435,79468140613244910123845191415450928
0.25258,25016,229326321,01836,08682141301611763372514598227426560942
0.55010,24116,460406423,88536,405931424921191816640258156288434648958
0.757512,08316,950476628,26237,14911014568302641169054353209344451772984
0.87587.513,43217,175526730,38737,415119146823532213711166435258386460837996
110014,33617,231566733,25437,6431301479738378150128755002934164639191,007
PCRAS
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
Seconds
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
m Seconds
Aggr/Sngl
Aggr/Hier
Inher/Sngl
Inher/Hier
Percentage Classes to Retrieve
m Joules
-
45
Broadcasting Object Organization on the Air Channel
Organizing data objects on the air channel as a means to reduceaccess latency.
An appropriate data placement algorithm should attempt todetect data locality and cluster related data close to one another.
The objects in an object-oriented paradigm are normallyassociated with one another through semantic links ─inheritance, aggregation, or association.
An object-clustering algorithm takes advantage of suchrelationships and attempts to map a complex object into a linearsequence of objects along the semantic links.
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Object Organization on the Air Channel Object clustering to minimize the access delay ─
Taking object connectivity (degree of dependence amongobjects) into account.
How to map a weighted graph (complex object) onto a onedimensional air channel to reduce access latency?
Cluster Objects Based on connectivity: Strict Linearity ─ ApproximateLinearOrder Varying Levels of Connectivity ─ PartiallyLinearOrder
Issues of concern: Linearity Replication
46
Broadcasting
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47
Broadcasting
Object Organization on the Air Channel A complex object can be expressed as a
hierarchy or a directed acyclic graph (DAG) inwhich objects are represented as the nodes andlinks are the relationships among these objects.
Within the scope of disk storage medium, it hasbeen shown that clustering objects based ontheir semantic connectivity can improve theresponse time by an order of magnitude.
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Broadcasting
Object Organization on the Air Channel ─ AnExample
dcb
hgfe
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2
2
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3
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1
11
1
1
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a
2
Clustering Method Resulting Sequence
Depth First abensofgpqhrmcijdkl
Breadth First abrcdefgqhijklmnsop
Children- Depth First abrcdefgqhmnsopijkl
Level Clustering acibgqprmenosjdlkfh
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49
Broadcasting
Object Organization on the Air Channel ─ DifferentClustering Methods
Clustering Method Resulting Sequence
Depth First abensofgpqhrmcijdkl
Breadth First abrcdefgqhijklmnsop
Children- Depth First abrcdefgqhmnsopijkl
Level Clustering acibgqprmenosjdlkfh
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50
Broadcasting
Object Organization on the Air Channel In spite of the differences between a disk
and an air channel, from a databaseperspective, the goal in organizinginformation on the air channel is still thesame as that of the disk ─ to reduce theresponse time for accessing a series ofobjects requested.
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Broadcasting
Object Organization on the Air Channel In order to achieve this goal, the object organization on
an air channel has to meet the following three criteria: Linear ordering: The air channel is a one-dimensional sequential
access structure. This fact requires that the object ordering be linear. Minimum linear distance between related objects: multiple objects
might be retrieved based on their connection patterns. Reducing thedistance among these objects along the broadcast reduces the responsetime and power consumption.
More availability for popular objects: Generally, requests to datafollow the 20/80 rule, providing more availability for popular objectscan be achieved by simply replicating such objects .
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52
Broadcasting
Object Organization on the Air Channel ─ AnExample a
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-
53
Broadcasting
Object Organization on the Air Channel ─ AnExample Linear Individual Costs Total
Sequence ab ac ad ae bf bg bh ch cj ei ij Cost1 abfgchdeij 1 4 6 7 1 2 4 1 5 1 1 332 abfgcheijd 1 4 9 6 1 2 4 1 4 1 1 343 abcdefghij 1 2 3 4 4 5 6 5 7 4 1 42
4 abgfeichjd 1 6 9 4 2 1 6 1 2 1 3 365 acdeijbhgf 6 1 2 3 3 2 1 6 4 1 1 30
6 adeicjbhgf 6 4 1 2 3 2 1 3 1 1 2 26
7 adecbihgfj 4 3 1 2 4 3 2 3 6 3 4 358 adecbhgfij 4 3 1 2 3 2 1 2 6 6 1 319 adecijbhgf 6 3 1 2 3 2 1 4 2 2 1 27
10 adbfgcheij 2 5 1 7 1 2 4 1 4 1 1 2911 adceijbhgf 6 2 1 3 3 2 1 5 3 1 1 2812 aeidcjbhgf 6 4 3 1 3 2 1 3 1 1 3 2813 aedcbihgfj 4 3 2 1 4 3 2 3 6 4 4 3614 aedcijbhgf 6 3 2 1 3 2 1 4 2 3 1 28
a
edcb
i
j
hgf
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54
Broadcasting
Object Organization on the Air Channel ─ An Example Refer to the previous table, the abfgchdeij sequence objects a and
d are separated by the sequence bfgch and thus have a cost of 6. The right-most column represents the total cost associated with
each individual linear sequence. An optimal sequence is the linear sequence with the minimum total
sum. In a query where multiple related objects are retrieved, a minimum
average linear distance translates into smaller average responsetime. In this example, the optimum linear sequence achieves atotal sum of 26.
-
55
Object Organization on the Air Channel One method in obtaining an optimal linear sequence is
to enumerate and calculate all possible linear sequenceswith their associated costs and then choose thesequence with the minimum cost.
Naturally, such a solution, though simple, iscomputationally impractical.
In practice heuristic rules are used to generate a linearsequence with a reasonable cost.
Broadcasting
-
56
Object Organization on the Air Channel ─ StrictLinearity ─ ApproximateLinearOrder
Independent Node: An independent node is a nodethat has either one or no parent.
In example on slide 52, node e is an independent nodewhereas node h is not.
A graph containing only independent nodes makes up aforest.
Broadcasting
-
57
Object Organization on the Air Channel ─ Strict Linearity ─ApproximateLinearOrder Prioritize node based on their number of descendants in
ascending order — the node with the least number ofdescendants is given a higher priority.
Once a node is selected, all of its descendants should bevisited and placed on the sequence in a depth firstmanner, without any interruption from breadth siblings.
If a node has a non-independent child, with all of itsparents already visited, the non-independent childshould be inserted in the linear sequence before anyindependent child.
Broadcasting
-
58
Object Organization on the Air Channel ─ Strict Linearity ─ApproximateLinearOrder ApproximateLinearOrder Algorithm
Traverse DAG using DFS traversal and as each node is traversed Append the traversed node N to the sequence Remove N from {nodes to be traversed} if {non-independent children of N having all their parents in the sequence} ≠ ∅ Set ← {non-independent children of N having all their parents in
the sequence} else if {independent children of N} ≠ ∅ Set ← {independent children of N} NextNode ← node ∈ Set | node has least # of descendants among
the nodes in Set.
Broadcasting
-
59
Object Organization on the Air Channel ─ Strict Linearity ─ApproximateLinearOrder
The algorithm assumes a greedy strategy andstarts by selecting a node with an in-degree ofzero and out-degree of at least one.
Applying ApproximateLinearOrder algorithm to thegraph of slide 52 generates either the fifth or eleventhsequence (slide 53). This is dependent on whether c ord was chosen first as the child with the least number ofindependent-children.
Broadcasting
-
60
Object Organization on the Air Channel ─ Varying Levels ofConnectivity ─ PartiallyLinearOrder
In a complex object, objects are connected throughsemantic links with different degrees of connectivity.The frequency of accesses of objects in an object-oriented database reveals that some patterns are morefrequently traversed than others.
The algorithm PartiallyLinearOrder assumes a weightedDAG as its input and produces a linear sequence.
Broadcasting
-
61
Object Organization on the Air Channel ─ Varying Levels ofConnectivity ─ PartiallyLinearOrder The algorithm combines the nodes (single_node) of the
graph into multi_nodes in a descending order of theirconnectivity.
The insertion of single_nodes within a multi_noderespects the linear order at the granularity level of thesingle_nodes.
The multi_nodes are merged (with multi_nodes orsingle_nodes) at the multi_node granularity,recursively, without interfering with internal orderingsequences of a multi_node.
Broadcasting
-
62
Object Organization on the Air Channel ─ Varying Levels of Connectivity ─PartiallyLinearOrder PariallyLinearOrder Algorithm
for every weight ws in descending order for every two nodes N1 & N2 connected by ws merge Ni & Nj into one multi_node for every multi_node MN wm = ws - 1 for every weight wm in descending order while ∃ adjacent_node AN connected to MN if ∃ an edge in both directions between MN & AN compute WeightedLinearDistanceMN_AN & WeightedLinearDistanceAN_MN merge MN & AN into one multi_node, based on the appropriate direction
Broadcasting
-
63
Object Organization on the Air Channel ─ VaryingLevels of Connectivity ─ PartiallyLinearOrder
a
edcb
i
j
hgf
3
3
3
32 2
1
2
1
21
Original Graph
Broadcasting
-
64
Object Organization on the Air Channel ─ VaryingLevels of Connectivity ─ PartiallyLinearOrder
ach
edbf
ijg
2
1
2
2
21
1
First and Second iterations
b f g a c h e i j d
Third iteration
Broadcasting
a
edcb
i
j
hgf
3
3
3
32 2
1
2
1
21
Original Graph
-
65
Object Organization on the Air Channel
0
2
4
6
8
10
12
14
16
400 1200 2000 2800 3600 4400 5200 6000 6800 7600
Number of Objects
Ave
rage
Acc
ess D
elay
(Sec
.)
Children Depth First
PartLinOrder
ApproxLinOrder
Broadcasting
Chart4
4004000.5151290894
8008000.9710245132
120012001.5323934555
160016001.9695863724
200020002.4386920929
240024002.9068460464
280028003.397146225
320032004.0070075989
360036004.4064083099
400040004.8279161453
440044005.3714294434
480048005.8468732834
520052006.3271303177
560056006.8458423615
600060007.3416957855
640064007.6775436401
680068008.2197856903
720072008.6224727631
760076009.2089147568
800080009.6173028946
Children Depth First
PartLinOrder
ApproxLinOrder
Number of Objects
Average Access Delay (Sec.)
0.7478065491
0.5956707001
1.4874181747
1.1758861542
2.167517662
1.7435445786
2.9210519791
2.3002843857
3.5640993118
2.880487442
4.3533496857
3.3522310257
5.039981842
3.919465065
5.5851917267
4.4843883514
6.4912242889
5.1224651337
7.1238555908
5.7068462372
7.8835411072
6.2830114365
8.609828949
6.8458805084
9.1740055084
7.470913887
10.0819225311
8.1295375824
10.5791149139
8.4140205383
11.2520189285
8.8864564896
12.088470459
9.5177173615
12.6827278137
9.9269456863
13.8358402252
10.5339832306
14.382311821
11.4190301895
num
Children Depth FirstPartLinOrderApproxLinOrder
4007841326246065401520.74780654910.59567070010.5151290894
8001559671123300610181931.48741817471.17588615420.9710245132
12002272807182823916068312.1675176621.74354457861.5323934555
16003062945241202320652612.92105197912.30028438571.9695863724
20003737229302041025571543.56409931182.8804874422.4386920929
24004564818351506930480494.35334968573.35223102572.9068460464
28005284804410985735621665.0399818423.9194650653.397146225
32005856498470222242016525.58519172674.48438835144.0070075989
36006806542537129446204546.49122428895.12246513374.4064083099
40007469904598406250624377.12385559085.70684623724.8279161453
44008266492658821556323527.88354110726.28301143655.3714294434
48009028060717842661308918.6098289496.84588050845.8468732834
52009619642783382166344779.17400550847.4709138876.3271303177
5600105716628524438717838610.08192253118.12953758246.8458423615
6000110930068822740769832610.57911491398.41402053837.3416957855
6400117985979318125805048811.25201892858.88645648967.6775436401
6800126756809980050861907012.0884704599.51771736158.2197856903
72001329880410409157904131812.68272781379.92694568638.6224727631
76001450793011045682965624713.835840225210.53398323069.2089147568
800015080947119737211008447314.38231182111.41903018959.6173028946
num
Children Depth First
PartLinOrder
ApproxOptimalLinOrder
Number of Objects
Average Access Delay (Sec.)
szd
Children Depth First
PartLinOrder
ApproxLinOrder
Number of Objects
Average Access Delay (Sec.)
ppo
Children Depth FirstOptPartialNonLinOrderApproxOptimalLinOrder
[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026
[6:0:0]137281089292800.0130920410.01038742070.0088500977
[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514
[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622
[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433
[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597
[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566
ppo
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
rpf
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
nnr
Children Depth FirstOptPartialNonLinOrderApproxOptimalLinOrder
107933497697995358334287.56597232826.65660190585.5631904602
209595106787911366030689.15060615547.51410770426.2971763611
30105313789311159745559810.0435047158.87981319437.110212326
401170221310260511837524611.16009998329.78518581397.9872570038
501329861510936628920197912.682547569310.42998123178.7756910324
6014458089129589311032098213.788308143612.35859966289.8428554535
7015546461129875891064783214.826260566712.385930061310.1545639038
8017761218144815321193682616.938417434713.810665130611.3838443756
nnr
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Percentage of Popular Objects
Average Access Time (Sec.)
odd
Children Depth FirstOptPartialNonLinOrderApproxOptimalLinOrder
11216248911069851936718011.599053382910.55703258518.9332389832
29103419791314465327088.68169689187.54656219486.2300758362
39918981702788957710399.45947742466.70231723795.5036916733
4113699576250675552417110.84323596955.96110820775.2682600021
5134725666299645535259812.84844017036.0078096395.1046352386
6174224376498565573499716.61533069616.1975145345.4693193436
7202213556358444575043519.28458690646.06388473515.4840421677
8232566816607216566337222.17929935467.56135864266.4812149048
9281224646589300585980026.81967163097.54085540776.7060089111
10318375736789236616841830.36267566687.76966400157.0591941833
11354526687325979679163933.81029891979.08257741938.4201151848
12387994127758327673673437.00200271619.61859235768.3520452499
13420993867289194683855740.14910316479.73212394719.1304586411
14446474467711117697278842.579122543310.29545192729.3096763611
15469614898059058682263644.785965919510.76000328069.1092018127
16492587447744274704858646.976799011210.33972129829.4108776093
17509483778086274725370748.588158607510.79634056099.6847436905
18537894318216695752828351.297598838810.970471382110.0513422012
19556176148585816837277653.041090011611.463301086411.1788619995
20593043719012513812953056.557055473312.033003044110.8540935516
21605685229380549843758057.762643814112.524384117111.2653846741
22629764289074864866869960.059001922612.116250610411.5739618301
23651223539913259909787262.1055154813.235628700312.1469696045
246822773310748818928350765.067036628714.351220321712.3948190689
odd
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Replication Frequency
Average Access Delay (Sec.)
lvd
Children Depth FirstOptPartialNonLinOrderApproxOptimalLinOrder
[10:0]8582447620261447057768.18485927585.91527366644.48777771
[9:1]8925420683237055985998.51194381716.51585578925.3392400742
[8:2]9078371735027162695378.65780925757.00976467135.9790964127
[7:3]9902814797414969286549.44405937197.60474109656.6076793671
[6:4]10415394848860678786209.93289375318.09536552437.5136375427
[5:5]105550269349764835168010.06605720528.91662979137.9647827148
[4:6]111256129786678931271110.61021041879.33330345158.8812932968
[3:7]1171207310558765992937611.16950321210.06962299359.4693908691
[2:8]11923337108815171063257511.370980262810.377423286410.1400136948
[1:9]12613283115871981146988912.028964042711.050413131710.9385385513
[0:10]14715399144043841445763214.03369808213.737091064513.7878723145
lvd
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
bwd
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
Children Depth FirstOptPartialNonLinOrderApproxOptimalLinOrder
[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145
[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152
[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109
[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296
[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
Children Depth First
OptPartialNonLinOrder
ApproxOptimalLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
AverageWeakNormalStrong
100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748
200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768
300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455
400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701
500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287
Average
Weak
Normal
Strong
Number of Objects
Average Access Delay (Sec.)
64K128K256K512K1M2M
4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447
800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566
1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278
1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862
2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464
2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232
2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125
3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994
3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155
4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727
4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217
4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417
52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588
56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807
60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928
64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201
68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452
72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815
76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784
800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473
64K
128K
256K
512K
1M
2M
Number of Objects
Average Access Delay (Sec.)
-
66
Object Organization on the Air Channel
0
5
10
15
20
25
[2:2:2] [6:0:0] [0:6:0] [0:0:6] [3:3:0] [3:0:3] [0:3:3]
Object Size Distribution [S:M:L]
Ave
rage
Acc
ess D
elay
(Sec
.)
Children Depth FirstPartLinOrderApproxLinOrder
Broadcasting
Chart5
[2:2:2][2:2:2][2:2:2]
[6:0:0][6:0:0][6:0:0]
[0:6:0][0:6:0][0:6:0]
[0:0:6][0:0:6][0:0:6]
[3:3:0][3:3:0][3:3:0]
[3:0:3][3:0:3][3:0:3]
[0:3:3][0:3:3][0:3:3]
Children Depth First
PartLinOrder
ApproxLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
9.1349954605
6.9946079254
5.9988327026
0.013092041
0.0103874207
0.0088500977
4.1759986877
3.4000377655
2.8636579514
22.2481927872
17.6374282837
15.1309728622
2.1842899323
1.6816511154
1.4196281433
11.4748239517
8.9566307068
7.5982427597
13.4513454437
10.7001314163
8.9345817566
num
Children Depth FirstPartLinOrderApproxLinOrder
4007841326246065401520.74780654910.59567070010.5151290894
8001559671123300610181931.48741817471.17588615420.9710245132
12002272807182823916068312.1675176621.74354457861.5323934555
16003062945241202320652612.92105197912.30028438571.9695863724
20003737229302041025571543.56409931182.8804874422.4386920929
24004564818351506930480494.35334968573.35223102572.9068460464
28005284804410985735621665.0399818423.9194650653.397146225
32005856498470222242016525.58519172674.48438835144.0070075989
36006806542537129446204546.49122428895.12246513374.4064083099
40007469904598406250624377.12385559085.70684623724.8279161453
44008266492658821556323527.88354110726.28301143655.3714294434
48009028060717842661308918.6098289496.84588050845.8468732834
52009619642783382166344779.17400550847.4709138876.3271303177
5600105716628524438717838610.08192253118.12953758246.8458423615
6000110930068822740769832610.57911491398.41402053837.3416957855
6400117985979318125805048811.25201892858.88645648967.6775436401
6800126756809980050861907012.0884704599.51771736158.2197856903
72001329880410409157904131812.68272781379.92694568638.6224727631
76001450793011045682965624713.835840225210.53398323069.2089147568
800015080947119737211008447314.38231182111.41903018959.6173028946
num
Children Depth First
PartLinOrder
ApproxOptimalLinOrder
Number of Objects
Average Access Delay (Sec.)
szd
Children Depth First
PartLinOrder
ApproxLinOrder
Number of Objects
Average Access Delay (Sec.)
ppo
Children Depth FirstPartLinOrderApproxLinOrder
[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026
[6:0:0]137281089292800.0130920410.01038742070.0088500977
[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514
[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622
[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433
[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597
[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566
ppo
Children Depth First
OptPartialNonLinOrder
ApproxLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
rpf
Children Depth First
PartLinOrder
ApproxLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
nnr
Children Depth FirstPartLinOrderApproxLinOrder
107933497697995358334287.56597232826.65660190585.5631904602
209595106787911366030689.15060615547.51410770426.2971763611
30105313789311159745559810.0435047158.87981319437.110212326
401170221310260511837524611.16009998329.78518581397.9872570038
501329861510936628920197912.682547569310.42998123178.7756910324
6014458089129589311032098213.788308143612.35859966289.8428554535
7015546461129875891064783214.826260566712.385930061310.1545639038
8017761218144815321193682616.938417434713.810665130611.3838443756
nnr
Children Depth First
PartLinOrder
ApproxLinOrder
Percentage of Popular Objects
Average Access Time (Sec.)
odd
Children Depth FirstPartLinOrderApproxLinOrder
11216248911069851936718011.599053382910.55703258518.9332389832
29103419791314465327088.68169689187.54656219486.2300758362
39918981702788957710399.45947742466.70231723795.5036916733
4113699576250675552417110.84323596955.96110820775.2682600021
5134725666299645535259812.84844017036.0078096395.1046352386
6174224376498565573499716.61533069616.1975145345.4693193436
7202213556358444575043519.28458690646.06388473515.4840421677
8232566816607216566337222.17929935467.56135864266.4812149048
9281224646589300585980026.81967163097.54085540776.7060089111
10318375736789236616841830.36267566687.76966400157.0591941833
11354526687325979679163933.81029891979.08257741938.4201151848
12387994127758327673673437.00200271619.61859235768.3520452499
13420993867289194683855740.14910316479.73212394719.1304586411
14446474467711117697278842.579122543310.29545192729.3096763611
15469614898059058682263644.785965919510.76000328069.1092018127
16492587447744274704858646.976799011210.33972129829.4108776093
17509483778086274725370748.588158607510.79634056099.6847436905
18537894318216695752828351.297598838810.970471382110.0513422012
19556176148585816837277653.041090011611.463301086411.1788619995
20593043719012513812953056.557055473312.033003044110.8540935516
21605685229380549843758057.762643814112.524384117111.2653846741
22629764289074864866869960.059001922612.116250610411.5739618301
23651223539913259909787262.1055154813.235628700312.1469696045
246822773310748818928350765.067036628714.351220321712.3948190689
odd
Children Depth First
PartLinOrder
ApproxLinOrder
Replication Frequency
Average Access Delay (Sec.)
lvd
Children Depth FirstPartLinOrderApproxLinOrder
[10:0]8582447620261447057768.18485927585.91527366644.48777771
[9:1]8925420683237055985998.51194381716.51585578925.3392400742
[8:2]9078371735027162695378.65780925757.00976467135.9790964127
[7:3]9902814797414969286549.44405937197.60474109656.6076793671
[6:4]10415394848860678786209.93289375318.09536552437.5136375427
[5:5]105550269349764835168010.06605720528.91662979137.9647827148
[4:6]111256129786678931271110.61021041879.33330345158.8812932968
[3:7]1171207310558765992937611.16950321210.06962299359.4693908691
[2:8]11923337108815171063257511.370980262810.377423286410.1400136948
[1:9]12613283115871981146988912.028964042711.050413131710.9385385513
[0:10]14715399144043841445763214.03369808213.737091064513.7878723145
lvd
Children Depth First
PartLinOrder
ApproxLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
bwd
Children Depth First
PartLinOrder
ApproxLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
Children Depth FirstPartLinOrderApproxLinOrder
[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145
[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152
[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109
[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296
[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205
Children Depth First
PartLinOrder
ApproxLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
Children Depth First
PartLinOrder
ApproxLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
AverageWeakNormalStrong
100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748
200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768
300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455
400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701
500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287
Average
Weak
Normal
Strong
Number of Objects
Average Access Delay (Sec.)
64K128K256K512K1M2M
4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447
800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566
1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278
1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862
2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464
2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232
2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125
3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994
3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155
4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727
4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217
4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417
52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588
56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807
60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928
64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201
68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452
72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815
76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784
800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473
64K
128K
256K
512K
1M
2M
Number of Objects
Average Access Delay (Sec.)
-
67
Object Organization on the Air Channel
0
2
4
6
8
10
12
14
16
[10:0] [9:1] [8:2] [7:3] [6:4] [5:5] [4:6] [3:7] [2:8] [1:9] [0:10]
Next-Node Ratio [C:R]
Ave
rage
Acc
ess D
elay
(Sec
.)
Children Depth FirstPartLinOrderApproxLinOrder
Broadcasting
Chart6
[10:0][10:0][10:0]
[9:1][9:1][9:1]
[8:2][8:2][8:2]
[7:3][7:3][7:3]
[6:4][6:4][6:4]
[5:5][5:5][5:5]
[4:6][4:6][4:6]
[3:7][3:7][3:7]
[2:8][2:8][2:8]
[1:9][1:9][1:9]
[0:10][0:10][0:10]
Children Depth First
PartLinOrder
ApproxLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
8.1848592758
5.9152736664
4.48777771
8.5119438171
6.5158557892
5.3392400742
8.6578092575
7.0097646713
5.9790964127
9.4440593719
7.6047410965
6.6076793671
9.9328937531
8.0953655243
7.5136375427
10.0660572052
8.9166297913
7.9647827148
10.6102104187
9.3333034515
8.8812932968
11.169503212
10.0696229935
9.4693908691
11.3709802628
10.3774232864
10.1400136948
12.0289640427
11.0504131317
10.9385385513
14.033698082
13.7370910645
13.7878723145
num
Children Depth FirstPartLinOrderApproxLinOrder
4007841326246065401520.74780654910.59567070010.5151290894
8001559671123300610181931.48741817471.17588615420.9710245132
12002272807182823916068312.1675176621.74354457861.5323934555
16003062945241202320652612.92105197912.30028438571.9695863724
20003737229302041025571543.56409931182.8804874422.4386920929
24004564818351506930480494.35334968573.35223102572.9068460464
28005284804410985735621665.0399818423.9194650653.397146225
32005856498470222242016525.58519172674.48438835144.0070075989
36006806542537129446204546.49122428895.12246513374.4064083099
40007469904598406250624377.12385559085.70684623724.8279161453
44008266492658821556323527.88354110726.28301143655.3714294434
48009028060717842661308918.6098289496.84588050845.8468732834
52009619642783382166344779.17400550847.4709138876.3271303177
5600105716628524438717838610.08192253118.12953758246.8458423615
6000110930068822740769832610.57911491398.41402053837.3416957855
6400117985979318125805048811.25201892858.88645648967.6775436401
6800126756809980050861907012.0884704599.51771736158.2197856903
72001329880410409157904131812.68272781379.92694568638.6224727631
76001450793011045682965624713.835840225210.53398323069.2089147568
800015080947119737211008447314.38231182111.41903018959.6173028946
num
Children Depth First
PartLinOrder
ApproxOptimalLinOrder
Number of Objects
Average Access Delay (Sec.)
szd
Children Depth First
PartLinOrder
ApproxLinOrder
Number of Objects
Average Access Delay (Sec.)
ppo
Children Depth FirstPartLinOrderApproxLinOrder
[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026
[6:0:0]137281089292800.0130920410.01038742070.0088500977
[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514
[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622
[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433
[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597
[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566
ppo
Children Depth First
OptPartialNonLinOrder
ApproxLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
rpf
Children Depth First
PartLinOrder
ApproxLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
nnr
Children Depth FirstPartLinOrderApproxLinOrder
107933497697995358334287.56597232826.65660190585.5631904602
209595106787911366030689.15060615547.51410770426.2971763611
30105313789311159745559810.0435047158.87981319437.110212326
401170221310260511837524611.16009998329.78518581397.9872570038
501329861510936628920197912.682547569310.42998123178.7756910324
6014458089129589311032098213.788308143612.35859966289.8428554535
7015546461129875891064783214.826260566712.385930061310.1545639038
8017761218144815321193682616.938417434713.810665130611.3838443756
nnr
Children Depth First
PartLinOrder
ApproxLinOrder
Percentage of Popular Objects
Average Access Time (Sec.)
odd
Children Depth FirstPartLinOrderApproxLinOrder
11216248911069851936718011.599053382910.55703258518.9332389832
29103419791314465327088.68169689187.54656219486.2300758362
39918981702788957710399.45947742466.70231723795.5036916733
4113699576250675552417110.84323596955.96110820775.2682600021
5134725666299645535259812.84844017036.0078096395.1046352386
6174224376498565573499716.61533069616.1975145345.4693193436
7202213556358444575043519.28458690646.06388473515.4840421677
8232566816607216566337222.17929935467.56135864266.4812149048
9281224646589300585980026.81967163097.54085540776.7060089111
10318375736789236616841830.36267566687.76966400157.0591941833
11354526687325979679163933.81029891979.08257741938.4201151848
12387994127758327673673437.00200271619.61859235768.3520452499
13420993867289194683855740.14910316479.73212394719.1304586411
14446474467711117697278842.579122543310.29545192729.3096763611
15469614898059058682263644.785965919510.76000328069.1092018127
16492587447744274704858646.976799011210.33972129829.4108776093
17509483778086274725370748.588158607510.79634056099.6847436905
18537894318216695752828351.297598838810.970471382110.0513422012
19556176148585816837277653.041090011611.463301086411.1788619995
20593043719012513812953056.557055473312.033003044110.8540935516
21605685229380549843758057.762643814112.524384117111.2653846741
22629764289074864866869960.059001922612.116250610411.5739618301
23651223539913259909787262.1055154813.235628700312.1469696045
246822773310748818928350765.067036628714.351220321712.3948190689
odd
Children Depth First
PartLinOrder
ApproxLinOrder
Replication Frequency
Average Access Delay (Sec.)
lvd
Children Depth FirstPartLinOrderApproxLinOrder
[10:0]8582447620261447057768.18485927585.91527366644.48777771
[9:1]8925420683237055985998.51194381716.51585578925.3392400742
[8:2]9078371735027162695378.65780925757.00976467135.9790964127
[7:3]9902814797414969286549.44405937197.60474109656.6076793671
[6:4]10415394848860678786209.93289375318.09536552437.5136375427
[5:5]105550269349764835168010.06605720528.91662979137.9647827148
[4:6]111256129786678931271110.61021041879.33330345158.8812932968
[3:7]1171207310558765992937611.16950321210.06962299359.4693908691
[2:8]11923337108815171063257511.370980262810.377423286410.1400136948
[1:9]12613283115871981146988912.028964042711.050413131710.9385385513
[0:10]14715399144043841445763214.03369808213.737091064513.7878723145
lvd
Children Depth First
PartLinOrder
ApproxLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
bwd
Children Depth First
PartLinOrder
ApproxLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
Children Depth FirstPartLinOrderApproxLinOrder
[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145
[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152
[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109
[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296
[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205
Children Depth First
PartLinOrder
ApproxLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
Children Depth First
PartLinOrder
ApproxLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
AverageWeakNormalStrong
100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748
200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768
300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455
400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701
500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287
Average
Weak
Normal
Strong
Number of Objects
Average Access Delay (Sec.)
64K128K256K512K1M2M
4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447
800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566
1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278
1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862
2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464
2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232
2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125
3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994
3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155
4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727
4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217
4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417
52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588
56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807
60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928
64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201
68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452
72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815
76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784
800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473
64K
128K
256K
512K
1M
2M
Number of Objects
Average Access Delay (Sec.)
-
68
Object Organization on the Air Channel
0
2
4
6
8
10
12
14
16
[9:0:0:0] [6:1:1:1] [1:6:1:1] [1:1:6:1] [1:1:1:6]Out-Degree Distribution [0:1:2:3]
Aver
age A
cces
s Dela
y (S
ec.) Children Depth First
PartLinOrderApproxLinOrder
Broadcasting
Chart7
[9:0:0:0][9:0:0:0][9:0:0:0]
[6:1:1:1][6:1:1:1][6:1:1:1]
[1:6:1:1][1:6:1:1][1:6:1:1]
[1:1:6:1][1:1:6:1][1:1:6:1]
[1:1:1:6][1:1:1:6][1:1:1:6]
Children Depth First
PartLinOrder
ApproxLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
14.033698082
13.7370910645
13.7878723145
11.3458595276
10.2944984436
9.8448181152
7.3045969009
4.7507419586
3.5127468109
7.3087825775
4.8800554276
3.252114296
6.91431427
4.3890419006
3.111738205
num
Children Depth FirstPartLinOrderApproxLinOrder
4007841326246065401520.74780654910.59567070010.5151290894
8001559671123300610181931.48741817471.17588615420.9710245132
12002272807182823916068312.1675176621.74354457861.5323934555
16003062945241202320652612.92105197912.30028438571.9695863724
20003737229302041025571543.56409931182.8804874422.4386920929
24004564818351506930480494.35334968573.35223102572.9068460464
28005284804410985735621665.0399818423.9194650653.397146225
32005856498470222242016525.58519172674.48438835144.0070075989
36006806542537129446204546.49122428895.12246513374.4064083099
40007469904598406250624377.12385559085.70684623724.8279161453
44008266492658821556323527.88354110726.28301143655.3714294434
48009028060717842661308918.6098289496.84588050845.8468732834
52009619642783382166344779.17400550847.4709138876.3271303177
5600105716628524438717838610.08192253118.12953758246.8458423615
6000110930068822740769832610.57911491398.41402053837.3416957855
6400117985979318125805048811.25201892858.88645648967.6775436401
6800126756809980050861907012.0884704599.51771736158.2197856903
72001329880410409157904131812.68272781379.92694568638.6224727631
76001450793011045682965624713.835840225210.53398323069.2089147568
800015080947119737211008447314.38231182111.41903018959.6173028946
num
Children Depth First
PartLinOrder
ApproxOptimalLinOrder
Number of Objects
Average Access Delay (Sec.)
szd
Children Depth First
PartLinOrder
ApproxLinOrder
Number of Objects
Average Access Delay (Sec.)
ppo
Children Depth FirstPartLinOrderApproxLinOrder
[2:2:2]9578737733437862902329.13499546056.99460792545.9988327026
[6:0:0]137281089292800.0130920410.01038742070.0088500977
[0:6:0]4378852356519830027634.17599868773.40003776552.8636579514
[0:0:6]23328921184941841586597522.248192787217.637428283715.1309728622
[3:3:0]2290394176333914885882.18428993231.68165111541.4196281433
[3:0:3]120322259391708796733511.47482395178.95663070687.5982427597
[0:3:3]1410475811219901936858813.451345443710.70013141638.9345817566
ppo
Children Depth First
OptPartialNonLinOrder
ApproxLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
rpf
Children Depth First
PartLinOrder
ApproxLinOrder
Object Size Distribution [S:M:L]
Average Access Delay (Sec.)
nnr
Children Depth FirstPartLinOrderApproxLinOrder
107933497697995358334287.56597232826.65660190585.5631904602
209595106787911366030689.15060615547.51410770426.2971763611
30105313789311159745559810.0435047158.87981319437.110212326
401170221310260511837524611.16009998329.78518581397.9872570038
501329861510936628920197912.682547569310.42998123178.7756910324
6014458089129589311032098213.788308143612.35859966289.8428554535
7015546461129875891064783214.826260566712.385930061310.1545639038
8017761218144815321193682616.938417434713.810665130611.3838443756
nnr
Children Depth First
PartLinOrder
ApproxLinOrder
Percentage of Popular Objects
Average Access Time (Sec.)
odd
Children Depth FirstPartLinOrderApproxLinOrder
11216248911069851936718011.599053382910.55703258518.9332389832
29103419791314465327088.68169689187.54656219486.2300758362
39918981702788957710399.45947742466.70231723795.5036916733
4113699576250675552417110.84323596955.96110820775.2682600021
5134725666299645535259812.84844017036.0078096395.1046352386
6174224376498565573499716.61533069616.1975145345.4693193436
7202213556358444575043519.28458690646.06388473515.4840421677
8232566816607216566337222.17929935467.56135864266.4812149048
9281224646589300585980026.81967163097.54085540776.7060089111
10318375736789236616841830.36267566687.76966400157.0591941833
11354526687325979679163933.81029891979.08257741938.4201151848
12387994127758327673673437.00200271619.61859235768.3520452499
13420993867289194683855740.14910316479.73212394719.1304586411
14446474467711117697278842.579122543310.29545192729.3096763611
15469614898059058682263644.785965919510.76000328069.1092018127
16492587447744274704858646.976799011210.33972129829.4108776093
17509483778086274725370748.588158607510.79634056099.6847436905
18537894318216695752828351.297598838810.970471382110.0513422012
19556176148585816837277653.041090011611.463301086411.1788619995
20593043719012513812953056.557055473312.033003044110.8540935516
21605685229380549843758057.762643814112.524384117111.2653846741
22629764289074864866869960.059001922612.116250610411.5739618301
23651223539913259909787262.1055154813.235628700312.1469696045
246822773310748818928350765.067036628714.351220321712.3948190689
odd
Children Depth First
PartLinOrder
ApproxLinOrder
Replication Frequency
Average Access Delay (Sec.)
lvd
Children Depth FirstPartLinOrderApproxLinOrder
[10:0]8582447620261447057768.18485927585.91527366644.48777771
[9:1]8925420683237055985998.51194381716.51585578925.3392400742
[8:2]9078371735027162695378.65780925757.00976467135.9790964127
[7:3]9902814797414969286549.44405937197.60474109656.6076793671
[6:4]10415394848860678786209.93289375318.09536552437.5136375427
[5:5]105550269349764835168010.06605720528.91662979137.9647827148
[4:6]111256129786678931271110.61021041879.33330345158.8812932968
[3:7]1171207310558765992937611.16950321210.06962299359.4693908691
[2:8]11923337108815171063257511.370980262810.377423286410.1400136948
[1:9]12613283115871981146988912.028964042711.050413131710.9385385513
[0:10]14715399144043841445763214.03369808213.737091064513.7878723145
lvd
Children Depth First
PartLinOrder
ApproxLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
bwd
Children Depth First
PartLinOrder
ApproxLinOrder
Next-Node Ratio [C:R]
Average Access Delay (Sec.)
Children Depth FirstPartLinOrderApproxLinOrder
[9:0:0:0]14715399144043841445763214.03369808213.737091064513.7878723145
[6:1:1:1]11896996107945641032304011.345859527610.29449844369.8448181152
[1:6:1:1]7659425498151436833827.30459690094.75074195863.5127468109
[1:1:6:1]7663814511710934100897.30878257754.88005542763.252114296
[1:1:1:6]7250184460224432628946.914314274.38904190063.111738205
Children Depth First
PartLinOrder
ApproxLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
Children Depth First
PartLinOrder
ApproxLinOrder
Out-Degree Distribution [0:1:2:3]
Average Access Delay (Sec.)
AverageWeakNormalStrong
100015348051648356162574012619831.46370410921.57199478151.55042648321.2035207748
200030149223216378318395625212632.87525367743.06737709053.03645706182.404463768
300044702324672483476584138608534.26314544684.45602703094.54506015783.6819963455
400060099316443940642542951499435.73151683816.14542007456.12776660924.9113683701
500074822587978466781818063651517.13563728337.60885810857.4559974676.0702810287
Average
Weak
Normal
Strong
Number of Objects
Average Access Delay (Sec.)
64K128K256K512K1M2M
4005401528.24206542974.12103271482.06051635741.03025817870.51512908940.2575645447
800101819315.53639221197.7681961063.8840980531.94204902650.97102451320.4855122566
1200160683124.518295288112.2591476446.1295738223.0647869111.53239345550.7661967278
1600206526131.51338195815.7566909797.87834548953.93917274481.96958637240.9847931862
2000255715439.019073486319.50953674329.75476837164.87738418582.43869209291.2193460464
2400304804946.509536743223.254768371611.62738418585.81369209292.90684604641.4534230232
2800356216654.354339599627.177169799813.58858489996.794292453.3971462251.6985731125
3200420165264.11212158232.05606079116.02803039558.01401519784.00700759892.0035037994
3600462045470.50253295935.251266479517.62563323978.81281661994.40640830992.203204155
4000506243777.246658325238.623329162619.31166458139.65583229064.82791614532.4139580727
4400563235285.942871093842.971435546921.485717773410.74285888675.37142944342.6857147217
4800613089193.549972534246.774986267123.387493133511.69374656685.84687328342.9234366417
52006634477101.23408508350.617042541525.308521270812.65426063546.32713031773.1635651588
56007178386109.533477783254.766738891627.383369445813.69168472296.84584236153.4229211807
60007698326117.467132568458.733566284229.366783142114.6833915717.34169578553.6708478928
64008050488122.840698242261.420349121130.710174560515.35508728037.67754364013.8387718201
68008619070131.516571044965.758285522532.879142761216.43957138068.21978569034.1098928452
72009041318137.95956420968.979782104534.489891052217.24494552618.62247276314.3112363815
76009656247147.342636108473.671318054236.835659027118.41782951359.20891475684.6044573784
800010084473153.876846313576.938423156738.469211578419.23460578929.61730289464.8086514473
64K
128K
256K
512K
1M
2M
Number of Objects
Average Access Delay (Sec.)
-
69
Object Organization on Parallel Channels The broadcast length is a factor that affects the
average response time in retrieving objectsfrom the air channel.
The broadcast length can be reduced if objectsare broadcast along the parallel air channels.
Reduced average response time could alsotranslate into lower power consumption.
Broadcasting
-
70
Object Organization on Parallel Channels Formally we are intended to assign the objects
from a weighted DAG onto multiple channels,while: Preserving dependency implied by the edges, Minimizing the overall broadcast time (load
balancing) and Clustering related objects close to one another
(improving the response time).
Broadcasting
-
71
Object Organization on Parallel Channels Assuming that all channels have the same data rate, one
can draw many analogies between object organizationon parallel channels and static task scheduling in ahomogeneous multiprocessor environment:
Tasks are represented as a directed graph D ≡ (N, A),where nodes (N) and directed edges (A) representingprocesses and dependence among the processes,respectively.
An optimal solution to such a problem is proven to beNP hard and hence, in many solutions, heuristics havebeen developed to generate a “suitable solution”.
Broadcasting
-
Object Organization on Parallel Channels We are intended to assign the objects from a weighted
DAG onto multiple channels, while: Preserving dependency implied by the edges, Minimizing the overall broadcast length (load balancing) and Clustering related objects close to one another (improving the
response time).
Largest Object First (LOF) Clustering Critical-Path (CCP)
72
Broadcasting
-
73
Object Organization on Parallel Channels ─Largest Object First This algorithm relies on a simple and localized
heuristic by giving priority to larger objects. Consider a 2-channel environment and three
objects A, B, and C with the followingrelationships among the sizes of the objects A >B > C.
Broadcasting
-
74
Object Organization on Parallel Channels ─ LargestObject First
B AC
AC B
Random allocation Allocation based on the Largest Object First Heuristic
Broadcasting
-
75
Object Organization on Parallel Channels ─ LargestObject First
The algorithm follows the following procedure;Recursively, a "proper" node with in-degree of zero ischosen (initially the root) and assigned to a "proper"channel.
A “proper” channel is the one with the smallest overallsize.
A “proper” node is the largest node with in-degree ofzero.
Broadcasting
-
76
Object Organization on Parallel Channels ─ LargestObject First Largest Object First Algorithm
Repeat until all nodes are assignedAssign a free node with the largest weight whose
parents are fully allocated to the least-loadedchannel
Remove all out-edges of assigned node from the dagInsert resulting free nodes into the list of free nodes.
Broadcasting
-
77
Object Organization on Parallel Channels ─ ClusteringCritical-Path
AssignWeights(DAG) Algorithm for every node i
Calculate Wi Weight of each node is calculated based on the:
Size of the node, Maximum weight of its children, Number of children with in-degree 1 and in-degree > 1, and Degree of connectivity among objects.
Broadcasting
-
78
Object Organization on Parallel Channels ─Clustering Critical-Path Critical Path Algorithm
AssignWeights(DAG) repeat until all the nodes have been processed
Select the free node N with the largest weight if all parents of N are fully allocated on the channels
place it on the currently least-loaded channel else
fill up the least-loaded channel(s) with nulls up to theend of the last allocated parent of N then place N on it.
Broadcasting
-
79
Object Organization on Parallel Channels
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
1 2 3 4 5 6 7 8
Number of Channels
Ave
rage
Res
pons
e Ti
me
Per O
bjec
t (S
ec.) LOF
CCP
Broadcasting
Chart1
5.99912643435.9991264343
3.03976608242.75
2.262
1.821.58
1.71.32
1.521.1428589004
1.461.053625241
1.41.0009916975
LOF
CCP
Number of Channels
Average Response Time Per Object (Sec.)
Sheet1
BADACE
CEBD
BADAD
CEBCE
BA
C
A
CB
C
DG
D
CG
NumChnnls
Response Single6290540
Delay Single6290232
Data Rate1048576
Previous WorkCurrent Work
LOFCCPRatio/SingleRatio/SingleCCP/LOF% ImprvNumChnnlsLOFCCPLOFCCPOODLOFCCPLOFCCPFRelatedRandomAvg. access delayRelatedRandomAvg. access delay
11257191257191.001.000.000.0016,290,5406,290,5406.006.00[5:1:1:1]1,622,1471,603,2731.551.5301,707,0001,896,8371,513,0951.631.811.44
26370257629.59887322871.972.180.1110.5423,187,4262,883,5843.042.75[3:3:1:1]1,761,6081,627,3901.681.550.11,707,0821,869,5441,522,5321.631.781.45
347361.052164907941912.43554416632.653.000.1313.0032,369,7822,097,1522.262.00[2:2:2:2]1,908,4081,656,7501.821.580.21,703,9361,842,2521,543,5041.631.761.47
438140.316345191333110.82407989143.303.800.1515.1941,908,4081,656,7501.821.58[1:5:1:1]1,929,3801,709,1791.841.630.31,702,8871,814,9601,543,3221.621.731.47
535625.570212541427662.20745914983.534.540.2928.7951,782,5791,384,1201.701.32[1:3:3:1]2,001,6271,799,3561.911.720.41,680,8671,787,6671,583,3501.601.701.51
631853.4510135664239503.955.250.3333.0061,593,8361,198,3741.521.14[1:1:5:1]2,098,2011,878,0002.001.790.51,656,7501,760,3751,656,6691.581.681.58
730596.0779472414220804.115.690.3938.5771,530,9211,104,8061.461.05[1:1:3:3]2,327,8391,920,9912.221.830.61,623,9131,733,0821,690,3051.551.651.61
829338.7048809164209774.295.990.4039.8681,468,0061,049,6161.401.00[1:1:1:5]2,708,4722,012,2172.581.920.71,616,0891,705,7901,723,8591.541.631.64
0.81,667,9131,678,4971,746,9281.591.601.67
0.91,706,0871,651,2051,762,6561.631.571.68
11,707,0001,623,9131,810,0001.631.551.73
NumChnnls
LOF
CCP
Number of channels
Average response time per object (Sec.)
Comparison
LOF
CCP
Out-degree distribution
Average response time per object (Sec.)
NumChannels
&A
Page &P
Related
Avg. access delay
Random
Factor of load balacing vs. clustering related objects
Average response time per object (Sec.)
Average access delay (Sec.)
&A
Page &P
Related
Random
Factor of load balancing vs. clustering related objects
Average response time per object (Sec.)
Basic Single6290540
Previous WorkCurrent Work
LOFCCPRatio/SingleRatio/SingleCCP/LOF% ImprvLOFCCP
11257191257191.001.000.000.006,290,5406,290,540
263702625001.972.010.021.923,187,4263,127,282
343642426002.882.950.022.452,183,6932,131,555
434125330003.683.810.033.411,707,4961,651,205
528835273004.364.610.065.621,442,8031,365,997
625818239504.875.250.087.801,291,8431,198,374
723901220805.265.690.088.251,195,9231,104,806
822740209775.535.990.088.401,137,8301,049,616
-
80
Object Organization on Parallel Channels
1.50
1.70
1.90
2.10
2.30
2.50
2.70
Aver
age R
espo
nse
Tim
e Per
Obj
ect
(Sec
.)
Out-Degree Distribution
LOF
CCP
Broadcasting
Chart2
[5:1:1:1][5:1:1:1]
[3:3:1:1][3:3:1:1]
[2:2:2:2][2:2:2:2]
[1:5:1:1][1:5:1:1]
[1:3:3:1][1:3:3:1]
[1:1:5:1][1:1:5:1]
[1:1:3:3][1:1:3:3]
[1:1:1:5][1:1:1:5]
LOF
CCP
Out-Degree Distribution
Average Response Time Per Object (Sec.)
1.547
1.529
1.68
1.552
1.82
1.58
1.84
1.63
1.9089
1.716
2.001
1.791
2.22
1.832
2.583
1.919
Sheet1
BADACE
CEBD
BADAD
CEBCE
BA
C
A
CB
C
DG
D
CG
NumChnnls
Response Single6290540
Delay Single6290232
Data Rate1048576
Previous WorkCurrent Work
LOFCCPRatio/SingleRatio/SingleCCP/LOF% ImprvNumChnnlsLOFCCPLOFCCPOODLOFCCPLOFCCPFRelatedRandomAvg. access delayRelatedRandomAvg. access delay