Near-Optimal Four-Cycle Counting in Graph Streams

TL;DR

This paper introduces a near-optimal 3-pass streaming algorithm for approximating the number of four-cycles in large graphs, improving space efficiency and matching theoretical lower bounds.

Contribution

The authors develop a 3-pass algorithm that achieves near-optimal space complexity for four-cycle counting in graph streams, surpassing previous methods.

Findings

Achieves $(1+\varepsilon)$-approximation with $ ilde{O}(m/\sqrt{T})$ space

Improves upon previous algorithms with higher space complexity

Matches the multi-pass lower bound for four-cycle counting

Abstract

We study four-cycle counting in arbitrary order graph streams. We present a 3-pass algorithm for $(1+\varepsilon)$-approximating the number of four-cycles using $\widetilde{O}(m/\sqrt{T})$ space, where $m$ is the number of edges and $T$ the number of four-cycles in the graph. This improves upon a 3-pass algorithm by Vorotnikova using space $\widetilde{O}(m/T^{1/3})$ and matches a multi-pass lower bound of $\Omega(m/\sqrt{T})$ by McGregor and Vorotnikova.