Parallel clique-like subgraph counting and listing

Abstract

Cliques and clique-like subgraphs (e.g., quasi-cliques) are important dense structures whose counting or listing are essential in applications like complex network analysis and community detection. These problems are usually solved by divide and conquer, where a task over a big graph can be recursively divided into subtasks over smaller subgraphs whose search spaces are disjoint. This divisible algorithmic paradigm brings enormous potential for parallelism, since different subtasks can run concurrently to drastically reduce the overall running time. In this paper, we explore this potential by proposing a unified framework for counting and listing clique-like subgraphs. We study how to divide and distribute the counting and listing tasks, and meanwhile, to balance the assigned workloads of each thread dynamically. Four applications are studied under our parallel framework, i.e., triangle counting, clique counting, maximal clique listing and quasi-clique listing. Extensive experiments are conducted which demonstrate that our solution achieves an ideal speedup on various real graph datasets.