Think Before You Discard: Accurate Triangle Counting in Graph Streams with Deletions

Abstract

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 edge additions and deletions. Compared to its best competitors, ThinkD is (a) Accurate: up to 4.3 $${\times }$$ more accurate within the same memory budget, (b) Fast: up to 2.2 $${\times }$$ faster for the same accuracy requirements, and (c) Theoretically sound: always maintaining unbiased estimates with small variances. Code related to this paper is available at: https://github.com/kijungs/thinkd .