Parallel five-cycle counting algorithms

Abstract

The frequency of given subgraphs in large graphs interests many research communities that use graphs to represent their data. However, subgraph counting is a challenging problem even with subgraph sizes as small as five due to combinatorial explosion. The first effort to count all five-vertex subgraphs in moderately large graphs of millions of edges did not occur until 2016. Among five-vertex patterns, the five-cycle is one of the most difficult to count. We design two new parallel five-cycle counting algorithms and prove that they are work-efficient and achieve polylogarithmic span. We implement the algorithms and perform a comprehensive evaluation of their performance. On a machine with 36 cores with two-way hyper-threading, our algorithm achieves 10-46x self-relative speed-up, and outperform the state-of-the-art serial algorithm by up to 818x.