Upper bounds and heuristics for the 2-club problem

Filipa D. Carvalho and M. Teresa Almeida

European Journal of Operational Research, 2011, vol. 210, issue 3, 489-494

Abstract: Given an undirected graph G = (V, E), a k-club is a subset of V that induces a subgraph of diameter at most k. The k-club problem is that of finding the maximum cardinality k-club in G. In this paper we present valid inequalities for the 2-club polytope and derive conditions for them to define facets. These inequalities are the basis of a strengthened formulation for the 2-club problem and a cutting plane algorithm. The LP relaxation of the strengthened formulation is used to compute upper bounds on the problem's optimum and to guide the generation of near-optimal solutions. Numerical experiments indicate that this approach is quite effective in terms of solution quality and speed, especially for low density graphs.

Keywords: Combinatorial; optimization; Integer; programming; k-club; problem; Heuristics (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:210:y:2011:i:3:p:489-494

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