Local and variable neighborhood search for the k-cardinality subgraph problem

Authors:
Jack Brimberg;Nenad Mladenović;Dragan Urošević
Affiliations:
Department of Business Administration, Royal Military College of Canada, Kingston, Canada;School of Mathematics, Brunel University, London, UK UB8 3PH;Mathematical Institute, Serbian Academy of Sciences, Belgrade, Serbia and Montenegro
Venue:
Journal of Heuristics
Year:
2008

Citing 5
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Abstract

The minimum weighted k-cardinality subgraph problem consists of finding a connected subgraph of a given graph with exactly k edges whose sum of weights is minimum. For this NP-hard combinatorial problem, only constructive types of heuristics have been suggested in the literature. In this paper we propose a new heuristic based on variable neighborhood search metaheuristic rules. This procedure uses a new local search developed by us. Extensive numerical results that include graphs with up to 5,000 vertices are reported. It appears that VNS outperforms all previous methods.