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

Author

Listed:
  • M Haouari

    (Ecole Polytechnique de Tunisie)

  • J Chaouachi

    (Ecole Polytechnique de Tunisie)

  • M Dror

    (University of Arizona)

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.

Suggested Citation

  • M Haouari & J Chaouachi & M Dror, 2005. "Solving the generalized minimum spanning tree problem by a branch-and-bound algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 382-389, April.
    • Handle: RePEc:pal:jorsoc:v:56:y:2005:i:4:d:10.1057_palgrave.jors.2601821
    DOI: 10.1057/palgrave.jors.2601821
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    References listed on IDEAS

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    1. Kansal, Anuraag R & Torquato, Salvatore, 2001. "Globally and locally minimal weight spanning tree networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 601-619.
    2. Feremans, Corinne & Labbe, Martine & Laporte, Gilbert, 2001. "On generalized minimum spanning trees," European Journal of Operational Research, Elsevier, vol. 134(2), pages 457-458, October.
    3. Dror, M. & Haouari, M. & Chaouachi, J., 2000. "Generalized spanning trees," European Journal of Operational Research, Elsevier, vol. 120(3), pages 583-592, February.
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    Cited by:

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    2. F. Carrabs & R. Cerulli & R. Pentangelo & A. Raiconi, 2018. "A two-level metaheuristic for the all colors shortest path problem," Computational Optimization and Applications, Springer, vol. 71(2), pages 525-551, November.
    3. Pop, Petrică C., 2020. "The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances," European Journal of Operational Research, Elsevier, vol. 283(1), pages 1-15.
    4. Pop, Petrică C. & Matei, Oliviu & Sabo, Cosmin & Petrovan, Adrian, 2018. "A two-level solution approach for solving the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 478-487.
    5. Oscar Danilo Montoya & Federico Martin Serra & Cristian Hernan De Angelo & Harold R. Chamorro & Lazaro Alvarado-Barrios, 2021. "Heuristic Methodology for Planning AC Rural Medium-Voltage Distribution Grids," Energies, MDPI, vol. 14(16), pages 1-20, August.

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