CrashSim: An Efficient Algorithm for Computing SimRank over Static - - PowerPoint PPT Presentation

April 22, 2020

CrashSim: An Efficient Algorithm for Computing SimRank over Static and Temporal Graphs

Mo Li1,2, Farhana M. Choudhury2, Renata Borovica-Gajic2, Zhiqiong Wang1, Junchang Xin1,*, Jianxin Li3

1Northeastern University, CN 2University of Melbourne, AU 3Deakin University, AU

Outline

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• Experimental Evaluation
• Conclusion

Experiments and Conclusion

• CrashSim Algorithm --- static graphs
• CrashSim-T Algorithm --- temporal graphs

Our Approach

• Preliminaries
• Problem Definition

Problem Definition

• SimRank Overview
• Motivation

Background

Background

• SimRank Overview
• Motivation

Background

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• Similarity assessment plays a vital role in our lives.

Recommender System Citation Graph Collaboration Network

Background

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• SimRank
• Node-to-node measurement based on the topology of graphs (KDD’02)
• Basic assumption
• Two nodes will be similar if they are both highly relevant to similar nodes
• Two Forms
• Original definition (KDD’02)
• √c- walk (SIGMOD’16)

Background

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• Temporal Graph
• Temporal SimRank queries: threshold and trend

A B C E D F G H A B C E D F G H A B C E D F G H

Recommender System

Problem Definition

• Preliminaries
• Problem Definition

Preliminaries

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SLING algorithm (SIGMOD’16) ProbeSim algorithm (VLDB’17)

Problem Definition

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Problem (Temporal SimRank Queries) Given: !, #, [%

&, % ']

Return: node set Ω, such that the SimRank of # and each node * ∈ Ω continuously meet a certain query requirement during the entire query interval [%

&, % ']

Problem (Temporal SimRank Trend Query) Given: !, #, [%

&, % ']

Return: node set Ω, such that the SimRank of # and each node * ∈ Ω is continuously increasing (or decreasing) during the entire query interval [%

&, % ']

Problem (Temporal SimRank Threshold Query) Given: !, #, [%

&, % '], ,

Return: node set Ω, such that the SimRank of # and each node * ∈ Ω is greater than

• during the entire query interval [%

&, % ']

Our Approach

• CrashSim Algorithm --- static graphs
• CrashSim-T Algorithm --- temporal graphs

CrashSim Algorithm

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• Motivation
• ProbeSim (VLDB’17) is the state-of-the-art algorithm for SimRak computation over static graph
• Drawbacks
• redundant computations
• the length of √"-walk determine the computation costs

A B C E D F G H

A B A B C D E C A D F G C D E A D F G H C B B C F G H E A D

CrashSim Algorithm

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• Key idea
• Constrain the length of √"-walk to lmax
• A reverse reachable tree of source u with the limited length of √"-walk, lmax
• Still obtain SimRank estimators with the same guaranteed error bound of the ProbeSim

Problem (Approximation Guarantee) Given: #, %, &, ' Return: ( %, ) such that |( %, ) − (,-(%, ))| ≤ & with at least 1 − ' probability

CrashSim Algorithm

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A B C E D F G H

A B C E B D H A E B

Level 0 Level 1 Level 2 Level 3

! 0,$ = 1 ! 1,' = ! 0,$ × ) * ' = 1×0.5 2 = 0.25 ! 1,. = ! 0,$ × ) * . = 1×0.5 3 = 0.167 ! 2,2 = 0.0625, ! 2,' = 0.0417, ! 2,4 = 0.0417 ! 3,5 = 0.0156, ! 3,$ = 0.0104 ! 3,2 = 0.0104, ! 3,' = 0.0104 In the k-th trial, 6 . = ., 4, ', $ 78 A, C = ! 0, C + ! 1, D + ! 2, B + ! 3, A = 0 + 0 + 0.0417 + 0.0104 = 0.0521

CrashSim Algorithm

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Time Complexity:

CrashSim-T Algorithm

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• Two opportunities
• Unnecessary to compute the SimRank between u and the candidate node set ! at each time instant
• The size of node set ! can only gradually reduce over time
• CrashSim naturally supports the computation of SimRank of the source u and a partial

set of nodes.

CrashSim-T Algorithm --- Delta Pruning

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• Affected area of a changed edge ! → #
• The altered nodes in the reverse reachable tree of u
• $%&' − 1 length reachable nodes of y
• Delta pruning: ignore the nodes of an unaffected area

A B C E D F G H A B C E D F G H

Delete * → +

A B C E B D

The reverse reachable tree of A remains unchanged.

CrashSim-T Algorithm --- Difference Pruning

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• Related area: the !"#$ length reverse reachable tree of u and v
• Difference pruning: filter out those nodes whose related area is unchanged

The reverse reachable tree of A and E remains unchanged. Add % → '

A B C E D F G H A B C E D F G H E B A D H

A B C E B D

CrashSim-T Algorithm

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• Main idea
• Check whether the conditions of delta and difference pruning are satisfied
• If so, disregard those nodes as part of the candidate node set
• Invoke CrashSim algorithm to compute u and residual nodes
• According to different query requirements to filter out unsatisfied nodes

Experiments and Conclusion

• Experimental Evaluation
• Conclusion

Experimental Evaluation

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• Datasets
• Comparison baselines
• SLING (SIGMOD’16), ProbeSim (VLDB’17), READS (VLDB’17)
• Setting and metrics
• ! varies from 0.0125, 0.025, 0.05 to 0.1
• "# = max ( ),+ − (-. ),+

+ ∈ 0

• 1234-(-56 =

7(9:)∩7(9=) >?@(9:,9=)

Experimental Evaluation

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(a) AS-733 (b) AS-Caidi (c) Wiki-Vote (d) HepTh (e) HepPh

Experimental Evaluation

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The impact of the query interval on the response time of the algorithms

Conclusion

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• Propose CrashSim algorithm, an index-free algorithm for single-source and partial

SimRank computation in static graphs

• Introduce CrashSim-T --- an extension to CrashSim to solve SimRank queries over

temporal graphs

• Experiments show that both CrashSim and CrashSim-T outperform the state-of-the-

art algorithms.

Thanks.

Mo Li limo_neucse@hotmail.com