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.
This work is supported by the National Science Foundation of China under grant number 60402011and the co-sponsored project of Beijing Committee of Education SYS100130422.
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Wu, B., Pei, X. (2007). A Parallel Algorithm for Enumerating All the Maximal k-Plexes. In: Washio, T., et al. Emerging Technologies in Knowledge Discovery and Data Mining. PAKDD 2007. Lecture Notes in Computer Science(), vol 4819. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77018-3_47
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DOI: https://doi.org/10.1007/978-3-540-77018-3_47
Publisher Name: Springer, Berlin, Heidelberg
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