Enumerating Maximal k-Plexes with Worst-Case Time Guarantee

2020-06-02

Proceedings of the AAAI Conference on Artificial Intelligence, 34

Volume

Vol. 34 No. 03: AAAI-20 Technical Tracks 3

AAAI Technical Track: Heuristic Search and Optimization

The problem of enumerating all maximal cliques in a graph is a key primitive in a variety of real-world applications such as community detection and so on. However, in practice, communities are rarely formed as cliques due to data noise. Hence, k-plex, a subgraph in which any vertex is adjacent to all but at most k vertices, is introduced as a relaxation of clique. In this paper, we investigate the problem of enumerating all maximal k-plexes and present FaPlexen, an enumeration algorithm which integrates the “pivot” heuristic and new branching schemes. To our best knowledge, for the first time, FaPlexen lists all maximal k-plexes with provably worst-case running time O(n2γn) in a graph with n vertices, where γ < 2. Then, we propose another algorithm CommuPlex which non-trivially extends FaPlexen to find all maximal k-plexes of prescribed size for community detection in massive real-life networks. We finally carry out experiments on both real and synthetic graphs and demonstrate that our algorithms run much faster than the state-of-the-art algorithms.

10.1609/aaai.v34i03.5625