DIST: Efficient k-Clique Listing via Induced Subgraph Trie

Abstract

Listing k-cliques plays a fundamental role in various data mining tasks, such as community detection and mining of cohesive substructures. Existing algorithms for the k-clique listing problem are built upon a general framework, which finds k-cliques by recursively finding (k-1)-cliques within subgraphs induced by the out-neighbors of each vertex. However, this framework has inherent inefficiency of finding smaller cliques within certain subgraphs repeatedly. In this paper, we propose an algorithm DIST for the k-clique listing problem. In contrast to existing works, the main idea in our approach is to compute each clique in the given graph only once and store it into a data structure called Induced Subgraph Trie, which allows us to retrieve the cliques efficiently. Furthermore, we propose a method to prune search space based on a novel concept called soft embedding of an l-tree, which further improves the running time. We show the superiority of our approach in terms of time and space usage through comprehensive experiments conducted on real-world networks; DIST outperforms the state-of-the-art algorithm by up to two orders of magnitude in both single-threaded and parallel experiments.