Journal of Combinatorial Optimization

, Volume 24, Issue 3, pp 347–373 | Cite as

Exact combinatorial algorithms and experiments for finding maximum k-plexes

  • Hannes Moser
  • Rolf Niedermeier
  • Manuel Sorge


We propose new practical algorithms to find maximum-cardinality k-plexes in graphs. A k-plex denotes a vertex subset in a graph inducing a subgraph where every vertex has edges to all but at most k vertices in the k-plex. Cliques are 1-plexes. In analogy to the special case of finding maximum-cardinality cliques, finding maximum-cardinality k-plexes is NP-hard. Complementing previous work, we develop exact combinatorial algorithms, which are strongly based on methods from parameterized algorithmics. The experiments with our freely available implementation indicate the competitiveness of our approach, for many real-world graphs outperforming the previously used methods.


Parameterized algorithmics Social network analysis Biological network analysis NP-complete graph problems Dense subgraphs s-plexes k-dependent sets 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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