Algorithms for the maximum k-club problem in graphs

Shahram Shahinpour () and Sergiy Butenko ()
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Shahram Shahinpour: Texas A&M University
Sergiy Butenko: Texas A&M University

Journal of Combinatorial Optimization, 2013, vol. 26, issue 3, No 11, 520-554

Abstract: Abstract Given a simple undirected graph G, a k-club is a subset of vertices inducing a subgraph of diameter at most k. The maximum k-club problem (MkCP) is to find a k-club of maximum cardinality in G. These structures, originally introduced to model cohesive subgroups in social network analysis, are of interest in network-based data mining and clustering applications. The maximum k-club problem is NP-hard, moreover, determining whether a given k-club is maximal (by inclusion) is NP-hard as well. This paper first provides a sufficient condition for testing maximality of a given k-club. Then it proceeds to develop a variable neighborhood search (VNS) heuristic and an exact algorithm for MkCP that uses the VNS solution as a lower bound. Computational experiments with test instances available in the literature show that the proposed algorithms are very effective on sparse instances and outperform the existing methods on most dense graphs from the testbed.

Keywords: Maximum k-club; Clique relaxations; Variable neighborhood search (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10878-012-9473-z

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