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

  • Theoretical Paper
  • Published:
Journal of the Operational Research Society

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.

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Acknowledgements

We would like to thank two anonymous referees for their valuable suggestions that have led to several improvements.

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Authors and Affiliations

  1. Ecole Polytechnique de Tunisie, La Marsa, Tunisia

    M Haouari & J Chaouachi

  2. University of Arizona, Tucson, AZ, USA

    M Dror

Authors
  1. M Haouari
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  2. J Chaouachi
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  3. M Dror
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Correspondence to M Haouari.

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Haouari, M., Chaouachi, J. & Dror, M. Solving the generalized minimum spanning tree problem by a branch-and-bound algorithm. J Oper Res Soc 56, 382–389 (2005). https://doi.org/10.1057/palgrave.jors.2601821

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  • DOI: https://doi.org/10.1057/palgrave.jors.2601821

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