Fast, Accurate and Provable Triangle Counting in Fully Dynamic Graph Streams

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Given a stream of edge additions and deletions, how can we estimate the count of triangles in it? If we can store only a subset of the edges, how can we obtain unbiased estimates with small variances? Counting triangles (i.e., cliques of size three) in a graph is a classical problem with applications in a wide range of research areas, including social network analysis, data mining, and databases. Recently, streaming algorithms for triangle counting have been extensively studied since they can naturally be used for large dynamic graphs. However, existing algorithms cannot handle edge deletions or suffer from low accuracy. Can we handle edge deletions while achieving high accuracy? We propose ThinkD, which accurately estimates the counts of global triangles (i.e., all triangles) and local triangles associated with each node in a fully dynamic graph stream with additions and deletions of edges. Compared to its best competitors, ThinkD is (a) Accurate: up to 4.3x more accurate within the same memory budget, (b) Fast: up to 2.2x faster for the same accuracy requirements, and (c) Theoretically sound: always maintaining estimates with zero bias (i.e., the difference between the true triangle count and the expected value of its estimate) and small variance. As an application, we use ThinkD to detect suddenly emerging dense subgraphs, and we show its advantages over state-of-the-art methods.
Publisher
ASSOC COMPUTING MACHINERY
Issue Date
2020-03
Language
English
Article Type
Article
Citation

ACM TRANSACTIONS ON KNOWLEDGE DISCOVERY FROM DATA, v.14, no.2, pp.1 - 39

ISSN
1556-4681
DOI
10.1145/3375392
URI
http://hdl.handle.net/10203/275049
Appears in Collection
RIMS Journal Papers
Files in This Item
3375392.pdf(3.54 MB)Download
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