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Branch-and-cut-and-price algorithms for the Degree Constrained Minimum Spanning Tree Problem

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  • Luis Bicalho
  • Alexandre Cunha
  • Abilio Lucena

Abstract

Assume that a connected undirected edge weighted graph G is given. The Degree Constrained Minimum Spanning Tree Problem (DCMSTP) asks for a minimum cost spanning tree of G where vertex degrees do not exceed given pre-defined upper bounds. In this paper, three exact solution algorithms are investigated for the problem. All of them are Branch-and-cut based and rely on the strongest formulation currently available for the problem. Additionally, to speed up the computation of dual bounds, they all use column generation, in one way or another. To test the algorithms, new hard to solve DCMSTP instances are proposed here. These instances, combined with additional ones taken from the literature, are then used in computational experiments. The experiments compare the new algorithms among themselves and also against the best algorithms currently available in the literature. As an outcome of them, one of the new algorithms stands out on top. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Luis Bicalho & Alexandre Cunha & Abilio Lucena, 2016. "Branch-and-cut-and-price algorithms for the Degree Constrained Minimum Spanning Tree Problem," Computational Optimization and Applications, Springer, vol. 63(3), pages 755-792, April.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:3:p:755-792
    DOI: 10.1007/s10589-015-9788-7
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    References listed on IDEAS

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    1. Volgenant, A., 1989. "A Lagrangean approach to the degree-constrained minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 39(3), pages 325-331, April.
    2. G. Dantzig & R. Fulkerson & S. Johnson, 1954. "Solution of a Large-Scale Traveling-Salesman Problem," Operations Research, INFORMS, vol. 2(4), pages 393-410, November.
    3. de Souza, Mauricio C. & Martins, Pedro, 2008. "Skewed VNS enclosing second order algorithm for the degree constrained minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 191(3), pages 677-690, December.
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    Cited by:

    1. Luiz Viana & Manoel Campêlo & Ignasi Sau & Ana Silva, 2021. "A unifying model for locally constrained spanning tree problems," Journal of Combinatorial Optimization, Springer, vol. 42(1), pages 125-150, July.
    2. Alexandre Salles Cunha, 2022. "Improved formulations and branch-and-cut algorithms for the angular constrained minimum spanning tree problem," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 379-413, August.
    3. Claudio Risso & Eduardo Canale, 2022. "Cost Optimized Design for the Local Wind Turbine Grid of an Onshore Wind Farm," Annals of Operations Research, Springer, vol. 316(2), pages 1187-1203, September.
    4. Chagas, Rosklin Juliano & Valle, Cristiano Arbex & da Cunha, Alexandre Salles, 2018. "Exact solution approaches for the Multi-period Degree Constrained Minimum Spanning Tree Problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 57-71.

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