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Finding a maximum k-club using the k-clique formulation and canonical hypercube cuts

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An Author Correction to this article was published on 07 June 2018

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Abstract

Detecting low-diameter clusters is an important graph-based data mining technique used in social network analysis, bioinformatics and text-mining. Low pairwise distances within a cluster can facilitate fast communication or good reachability between vertices in the cluster. Formally, a subset of vertices that induce a subgraph of diameter at most k is called a k-club. For low values of the parameter k, this model offers a graph-theoretic relaxation of the clique model that formalizes the notion of a low-diameter cluster. Using a combination of graph decomposition and model decomposition techniques, we demonstrate how the fundamental optimization problem of finding a maximum size k-club can be solved optimally on large-scale benchmark instances that are available in the public domain. Our approach circumvents the use of complicated formulations of the maximum k-club problem in favor of a simple relaxation based on necessary conditions, combined with canonical hypercube cuts introduced by Balas and Jeroslow.

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Change history

  • 07 June 2018

    This article provides an erratum to “Finding a maximum k-club using the k-clique formulation and canonical hypercube cuts,” published online in Optim Lett, 2015

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Acknowledgments

The authors would like to thank Dr. Alexander Veremyev for sharing the test-bed from [26] with us. We are also grateful to the referees for their helpful comments, and for pointing out the improved formulation in [27]. The computational experiments reported in this article were conducted at the Oklahoma State University High Performance Computing Center.

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Authors and Affiliations

  1. School of Industrial Engineering and Management, Oklahoma State University, Stillwater, OK, 74078, USA

    Esmaeel Moradi & Balabhaskar Balasundaram

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  1. Esmaeel Moradi
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  2. Balabhaskar Balasundaram
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Correspondence to Balabhaskar Balasundaram.

Additional information

Authors would like to acknowledge the support of the Air Force Office of Scientific Research Grant FA9550-12-1-0103 and the National Science Foundation Grant CMMI-1404971.

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Moradi, E., Balasundaram, B. Finding a maximum k-club using the k-clique formulation and canonical hypercube cuts. Optim Lett 12, 1947–1957 (2018). https://doi.org/10.1007/s11590-015-0971-7

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