Author

Quan-Quan C. Liu

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Preprint Sep 2026

Scalable Triangle Counting: The Threshold Algorithm

We study one-pass triangle counting on random-order edge streams. We present a remarkably simple algorithm---read edges from the stream until $Q$ triangles are observed in the prefix, then output $Q\,(m/S)^3$ where $S$ is the stopping length---and prove that, when the maximum number of triangles incident to any edge sa...

Asaf Etgar, A. Gilbert, Quan-Quan C. Liu et al. · 0 citations

Preprint Sep 2026

Parameter-Free Triangle Counting

Given an undirected, unweighted graph $G = (V,E)$ with $n$ vertices and $m$ edges, the triangle counting problem seeks the number of three-cycles in it. Triangle and subgraph counting are classical problems in graph algorithms, central to applications such as community detection, computing the clustering coefficient, m...

Asaf Etgar, A. Gilbert, Quan-Quan C. Liu et al. · 0 citations