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
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
The paper presents a one-pass algorithm in the insert-delete graph stream model that returns a $(1+\varepsilon)(\alpha+2)$-approximation for the size of the maximum matching in a graph of arboricity at most $\alpha$. The algorithm uses $O(\varepsilon^{-4/3}\alpha^{4/3}n^{2/3} \text{polylog} n)$ space. For constant $\al...
In contrast to the previous work, this analysis avoids consideration of fractional matchings and yields a significantly shorter and more direct proof of the approximation factor for the basic algorithm.
A. Mcgregor· 0 citations
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