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An exact and heuristic approach for the d-minimum branch vertices problem

Author

Listed:
  • Jorge Moreno

    (Universidade Federal Fluminense)

  • Yuri Frota

    (Universidade Federal Fluminense)

  • Simone Martins

    (Universidade Federal Fluminense)

Abstract

Given a connected graph $$G=(V,E)$$ G = ( V , E ) , the d-Minimum Branch Vertices (d-MBV) problem consists in finding a spanning tree of G with the minimum number of vertices with degree strictly greater than d. We developed a Miller–Tucker–Zemlin based formulation with valid inequalities for this problem. The results obtained for different values of d show the effectiveness of the proposed method, which has solved several instances faster than previous methods. Also, an heuristic is proposed for this problem, that was tested on several instances of the Minimum Branch Vertices problem, which is the d-MBV problem, when $$d = 2$$ d = 2 .

Suggested Citation

  • Jorge Moreno & Yuri Frota & Simone Martins, 2018. "An exact and heuristic approach for the d-minimum branch vertices problem," Computational Optimization and Applications, Springer, vol. 71(3), pages 829-855, December.
    • Handle: RePEc:spr:coopap:v:71:y:2018:i:3:d:10.1007_s10589-018-0027-x
    DOI: 10.1007/s10589-018-0027-x
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    References listed on IDEAS

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    1. Mercedes Landete & Alfredo Marín & José Luis Sainz-Pardo, 2017. "Decomposition methods based on articulation vertices for degree-dependent spanning tree problems," Computational Optimization and Applications, Springer, vol. 68(3), pages 749-773, December.
    2. R. Cerulli & M. Gentili & A. Iossa, 2009. "Bounded-degree spanning tree problems: models and new algorithms," Computational Optimization and Applications, Springer, vol. 42(3), pages 353-370, April.
    3. Rafael A. Melo & Phillippe Samer & Sebastián Urrutia, 2016. "An effective decomposition approach and heuristics to generate spanning trees with a small number of branch vertices," Computational Optimization and Applications, Springer, vol. 65(3), pages 821-844, December.
    4. Francesco Carrabs & Raffaele Cerulli & Manlio Gaudioso & Monica Gentili, 2013. "Lower and upper bounds for the spanning tree with minimum branch vertices," Computational Optimization and Applications, Springer, vol. 56(2), pages 405-438, October.
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