Covering K-Cliques in Billion-Scale Graphs

Kaiyu Chen, Dong Wen, Hanchen Wang, Zhengyi Yang, Wenjie Zhang, Xuemin Lin

Track: Graph algorithms and modeling for the Web

Keywords: clique, k-clique, clique cover, vertex cover, set cover

Abstract: The k-clique structure in graphs has been investigated in various real-world applications, such as community detection in complex networks, functional module discovery in biological networks, and link spam detection in web graphs. Despite extensive research on $k$-clique enumeration, the large number of k-cliques in many graphs poses a challenge for practical application and computation. To address this, we explore the $k$-clique $\tau$-cover problem, a generalization of the vertex cover problem. The problem aims to find a small set of vertices that can effectively represent all k-cliques in the graph. We prove the NP-hardness of finding the minimum k-clique cover. We propose a hierarchical solution that computes a small cover without enumerating k-cliques. Extensive experiments on real-world graphs verify the efficiency and effectiveness of our solution.

Submission Number: 646