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Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques

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  • Andreas M. Chwatal
  • Günther R. Raidl

Abstract

We present exact mixed integer programming approaches including branch-and-cut and branch-and-cut-and-price for the minimum label spanning tree problem as well as a variant of it having multiple labels assigned to each edge. We compare formulations based on network flows and directed connectivity cuts. Further, we show how to use odd-hole inequalities and additional inequalities to strengthen the formulation. Label variables can be added dynamically to the model in the pricing step. Primal heuristics are incorporated into the framework to speed up the overall solution process. After a polyhedral comparison of the involved formulations, comprehensive computational experiments are presented in order to compare and evaluate the underlying formulations and the particular algorithmic building blocks of the overall branch-and-cut- (and-price) framework.

Suggested Citation

  • Andreas M. Chwatal & Günther R. Raidl, 2011. "Solving the Minimum Label Spanning Tree Problem by Mathematical Programming Techniques," Advances in Operations Research, Hindawi, vol. 2011, pages 1-38, June.
    • Handle: RePEc:hin:jnlaor:143732
    DOI: 10.1155/2011/143732
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    Cited by:

    1. Thiago Gouveia da Silva & Serigne Gueye & Philippe Michelon & Luiz Satoru Ochi & Lucídio dos Anjos Formiga Cabral, 2019. "A polyhedral approach to the generalized minimum labeling spanning tree problem," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(1), pages 47-77, March.
    2. Silva, Thiago Gouveia da & Queiroga, Eduardo & Ochi, Luiz Satoru & Cabral, Lucídio dos Anjos Formiga & Gueye, Serigne & Michelon, Philippe, 2019. "A hybrid metaheuristic for the minimum labeling spanning tree problem," European Journal of Operational Research, Elsevier, vol. 274(1), pages 22-34.
    3. Raffaele Cerulli & Ciriaco D'Ambrosio & Domenico Serra & Carmine Sorgente, 2024. "The Budgeted Labeled Minimum Spanning Tree Problem," Mathematics, MDPI, vol. 12(2), pages 1-22, January.

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