Maximum k-Plex Finding: Choices of Pruning Techniques Matter!

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Abstract

A k-plex is a dense subgraph structure where every vertex can be disconnected with at most k vertices. Finding a maximum k-plex (MkP) in a big graph is a key primitive in many real applicati ons such as community detection and biological network analysis. A lot of MkP algorithms have been actively proposed in recent years in top AI and DB conferences, featuring a broad range of sophisticated pruning techniques. In this paper, we study the various pruning techniques from nine recent MkP algorithms including kPlexT, Maple, Seesaw, DiseMKP, kPlexS, KpLeX, Maplex, BnB and BS by unifying them in a common framework called U-MkP. We summarize their proposed techniques into three categories, those for (1) branching, (2) upper bounding, and (3) reduction during subgraph exploration. We find that different pruning techniques can have drastically different performance impacts, but there exists a configuration of the techniques dependent on k that leads to the best performance in vast majority of the time. Interestingly, extensive experiments with our unified framework reveal that some techniques are not effective as claimed in the original works, and we also discover an unmentioned technique that is actually the major performance booster when k > 5 . We also study problem variants such as finding all the MkPs and finding the densest MkP (i.e., with the most edges) to cover community diversity, and effective algorithm parallelization. Our source code is released at https://github.com/akhlaqueak/MKP-Study.