A parallel algorithm for enumerating all the maximal k-plexes

Authors:
Bin Wu;Xin Pei
Affiliations:
Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and Telecommunications, Beijing, China;Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and Telecommunications, Beijing, China
Venue:
PAKDD'07 Proceedings of the 2007 international conference on Emerging technologies in knowledge discovery and data mining
Year:
2007

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Abstract

Finding and enumerating subgraphs of different structures in a graph or a network is one of the fundamental problems in combinatorics. One of the earliest subgraph models is clique. However, the clique approach has been criticized for its overly restrictive nature. k-plex is one of the models which are introduced by weakening the requirement of clique. The problem to enumerate all the maximal k-plexes is NP complete. We consider this problem and propose an algorithm Pemp (Parallel Enumeration of all Maximal k-Plexes) for enumerating all the maximal k-plexes. We also propose a strategy to accelerate the pruning. A diameter pruning strategy is proposed. This strategy reduces the number of small maximal k-plexes and improves the performance greatly. We also state the parallel edition of our algorithm to analysis large networks and a load balancing strategy is given. In addition, we evaluate the performance of Pemp on random graphs.