Abstract
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.
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A preliminary version of this paper titled “Algorithms and experiments for clique relaxations—finding maximum s-plexes” appeared in the Proceedings of the 8th International Symposium on Experimental Algorithms (SEA 2009), June 3–6, 2009, Dortmund, Germany, vol. 5526 of Lecture Notes in Computer Science, pp. 233–244, Springer, 2009. Following a referee’s advice, we replaced “s-plexes” by the more common term “k-plexes”. The main work was done while all authors were with Friedrich-Schiller-Universität Jena.
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Moser, H., Niedermeier, R. & Sorge, M. Exact combinatorial algorithms and experiments for finding maximum k-plexes. J Comb Optim 24, 347–373 (2012). https://doi.org/10.1007/s10878-011-9391-5
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DOI: https://doi.org/10.1007/s10878-011-9391-5