ESCAPE: Efficiently Counting All Presented by: Omar Obeya 5 … · 2018. 4. 18. · ESCAPE:...
Transcript of ESCAPE: Efficiently Counting All Presented by: Omar Obeya 5 … · 2018. 4. 18. · ESCAPE:...
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ESCAPE: Efficiently Counting All 5-Vertex SubgraphsAuthors: Ali Pinar, C. Seshadhri, Vaidyanathan VishalPresented by: Omar Obeya
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Goal ● Count 5-vertex subgraphs○ Exact○ Scales
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New Problem: 21 5-vertex patterns
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Counting Patterns
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Counting Patterns
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Counting Patterns
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The Basics
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Key Idea: Cutting
● A Cut
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Key Idea: Cutting
● Not a Cut
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Fragments
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Shrinkage
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Fragments
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Shrinkage
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Algorithm
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Main Lemma
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Algorithm ● Pattern count in all graph = sum over all the possible cuts count of pattern - total number of shortage.
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Algorithm ● Account for automorphisms
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Example
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Example
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Example
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Algorithm ● Pattern count = 2*6 +1*6 - shrinkage
● Shrinkage = atomorphism * occurence = 2 * 2
● Answer = 18 - 4 = 14● Accounting for
automorphism = 14/2 = 7
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Example
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Example
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Results
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Performance
Comparison only with 4-vertex PGD
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Edge Prediction
Prob. for having another edge
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Subgraph Prediction
Ratio between patterns
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Future Work ● Scaling to 6-vertex subgraphs??!
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References ● Pinar, Ali, C. Seshadhri, and Vaidyanathan Vishal. "Escape: Efficiently counting all 5-vertex subgraphs." In Proceedings of the 26th International Conference on World Wide Web, pp. 1431-1440. International World Wide Web Conferences Steering Committee, 2017.