Solving the generalized minimum spanning tree problem by a branch-and-bound algorithm

M Haouari (), J Chaouachi and M Dror
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M Haouari: Ecole Polytechnique de Tunisie
J Chaouachi: Ecole Polytechnique de Tunisie
M Dror: University of Arizona

Journal of the Operational Research Society, 2005, vol. 56, issue 4, 382-389

Abstract: Abstract We present an exact algorithm for solving the generalized minimum spanning tree problem (GMST). Given an undirected connected graph and a partition of the graph vertices, this problem requires finding a least-cost subgraph spanning at least one vertex out of every subset. In this paper, the GMST is formulated as a minimum spanning tree problem with side constraints and solved exactly by a branch-and-bound algorithm. Lower bounds are derived by relaxing, in a Lagrangian fashion, complicating constraints to yield a modified minimum cost spanning tree problem. An efficient preprocessing algorithm is implemented to reduce the size of the problem. Computational tests on a large set of randomly generated instances with as many as 250 vertices, 1000 edges, and 25 subsets provide evidence that the proposed solution approach is very effective.

Keywords: minimum spanning tree; branch-and-bound: Lagrangian relaxation (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (5)

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DOI: 10.1057/palgrave.jors.2601821

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