lazy updates: an efficient technique to continuously monitoring reverse knn presented by: ying zhang...
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Lazy Updates: An Efficient Technique to Continuously Monitoring Reverse kNN
Presented By: Ying ZhangJoint work with
Muhammad Aamir Cheema, Xuemin Lin, Wei Wang, Wenjie Zhang
University of New South Wales, Australia1
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Reverse Nearest Neighbor• Nearest Neighbor Query (NN)
– Find the object closest to q
• Reverse Nearest Neighbor Query (RNN)– Korn et. al. Sigmod 2000– Find objects s.t. q is their NN
• Reverse k Nearest Neighbor Query (RkNN)– Find objects s.t. q is their kNN
p2 is the nearest neighbor of qp1 and p4 are the reverse nearest neighbors of q 2
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Applications
• Location based services,
• Location based games,
• Army strategic planning …
Continuous Monitoring of RkNN
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Related Work
• Continuous RNN and RkNN
– Benetis et. al (IDEAS 2002) : motion patterns (e.g., speed, direction) of objects and query are known
– Xia et. al (ICDE 2006) : continuous RNN without motion patterns
– Kang et. al (ICDE 2007) : improve the ICDE 2006 techniques
– Wu et. al (MDM 2008) : extend to RkNN monitoring
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Preliminaries• Half-space Pruning [VLDB04]
– Objects in the half-space containing a can be pruned
• Filtering– Repeat until no objects in
unpruned area
• Verification– p is RNN iff no object p’ s.t.
dist(p,p’) < dist( p,q) q
c
b
a
de
Static RNN query
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Unpruned area
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Preliminaries• Do filtering starting from the
existing “candidates” if – Query moves, or– Candidate objects move, or – An object moves to the
unpruned area
• Do verification
q
c
b
a
de
Continuous RNN query [ICDE07]
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Unpruned area
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Proposed Framework
• Assign rectangular safe regions to objects and queries
• Prune objects using safe regions
• Advantages
– Low Computation Cost
– Low Communication Cost
q
c b
a
d
e
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Challenges
R
Q
?
Based on : Shortest pair ?Longest pair ?Combination of them ?
NO
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Half-Space Pruning
qM N
p
mindist(x,MN) > dist(x,p)
x
Hp:M
Hp:N
x
x
– Any x on right side of LN :• mindist(x,MN) = dist(x,N)
– Hp:N : the half-space containing p and defined by the bisector between p and N
– Any x on left side of LM :• mindist(x,MN) = dist(x,M)
– Any x between LM and LN :• a parabola with mindist(x,
MN) = dist(x,p)
LMLN
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Challenges
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R
Q
?
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qM N
p
Hp:M
Hp:N
– Frontier point Fp
– Moved to Fp, the intersection of the half-spaces correctly bounds the pruned area
– Hp:N passing Fp : normalized half-space H’p:N
Half-Space Pruning: Normalization
Fp
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H’p:M
H’p:N
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Half-space Pruning: Pruning Rule 1
RM
N O
P
QD
A B
E
H’M:B
H’P:A
H’N:E
H’O:D
Fp
Pairs of antipodal corners are (B,M), (A,P), (E,N) and (D,O)
HM:B HP:A
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Dominance Pruning : pruning rule 2
RM
N O
P
QD
A B
C
H’M:B
H’P:A
H’N:C
H’O:D
Fp
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Trimming the rectangle
14
Q
RF1RF2
R
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Metric based pruning : pruning rule 3
Q
R
R’
maxdist(R,R’)
mindist(R’,Q)
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Order of pruning rules
Q
RF
R1
R2
R3
Fp
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Algorithm Overview• Initial Computation
– Filtering: Determine candidates– Verification: Verify each candidate
• Continuous Monitoring– Update candidate objects (filtering) if
• Query or a candidate moves out of safe region, or
• An object enters the unpruned area – Verify all candidates
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Illustration of Filtering
O3
Q
O2
O1
O4
O6
O5
O7
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Illustration of Verification
O3
Q
O2
O1
O4
O6
O5
O7
O1
O2
O3
O5
O6
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Q
?
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Data structure• Query table : id, safe region, candidate objects
• Object table : id, safe region
• Use grid data structure to support update
• Each cell c of the grid :– Object list : objects whose safe regions overlap c– Influence list : queries whose unpruned area
overlaps c
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Theoretical AnalysisCommunication Cost : |Q| x (M1 + M2 + 1) + M3
M1: # candidate objects
M2: #objects need exact location during the boolean range queries
M3: #objects that leave the safe regions
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N: Total number of objects w : width of the safe regionv: average speed of objects |Q| : The number of queries
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Experiment settings• Generate Moving objects and queries using Brinkhoff Generator [1] on
road map of Texas• Data space : 1000 Km X 1000 Km• Our algorithm (SAC) is compared with IGERN [2] for RNN queries and
CRkNN [3] for RkNN queries
[1] T. Brinkhoff. A framework for generating network-based moving objects. GeoInformatica, 2002.
[2] J. M. Kang, M. F. Mokbel, S. Shekhar, T. Xia, and D. Zhang. Continuous evaluation of monochromatic and bichromatic reverse nearest neighbors. ICDE, 2007.
[3] W. Wu, F. Yang, C. Y. Chan, and K.-L. Tan. Continuous reverse k-nearest-neighbor monitoring. MDM, 2008
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Evaluation of pruning rules
Avg. time for PR3 : 1.1 µs ( metric based pruning rule ) PR2 : 2.3 µs ( dominance pruning rule ) PR1 : 10.5 µs ( half space based pruning rule )
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Experiments: Size of safe region
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Experiments: Number of objects
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IGERN : ICDE 2007 work for RNNSAC : Our algorithm
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Experiments: Effect of data mobility
• Data mobility is the percentage of objects/queries that change their location within one time unit
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Experiments: RkNN queries
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CRkNN : MDM 2008 work for continuous monitoring RkNNSAC : Our algorithm
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Conclusion
Study the problem of continuously monitoring reverse kNN. Propose new framework based on safe region
Outperform previous algorithms in terms of computation cost and communication cost
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Thanks
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