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Decomposition methods based on articulation vertices for degree-dependent spanning tree problems

Author

Listed:
  • Mercedes Landete

    (Universidad Miguel Hernandez de Elche)

  • Alfredo Marín

    (Universidad de Murcia)

  • José Luis Sainz-Pardo

    (Universidad Miguel Hernandez de Elche)

Abstract

Decomposition methods for optimal spanning trees on graphs are explored in this work. The attention is focused on optimization problems where the objective function depends only on the degrees of the nodes of the tree. In particular, we deal with the Minimum Leaves problem, the Minimum Branch Vertices problem and the Minimum Degree Sum problem. The decomposition is carried out by identifying the articulation vertices of the graph and then its blocks, solving certain subproblems on the blocks and then bringing together the optimal sub-solutions following adequate procedures. Computational results obtained using similar Integer Programming formulations for both the original and the decomposed problems show the advantage of the proposed methods on decomposable graphs.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:3:d:10.1007_s10589-017-9924-7
    DOI: 10.1007/s10589-017-9924-7
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    References listed on IDEAS

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    1. Cerrone, C. & Cerulli, R. & Raiconi, A., 2014. "Relations, models and a memetic approach for three degree-dependent spanning tree problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 442-453.
    2. 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.
    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. 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.
    5. Fernandes, Lucinda Matos & Gouveia, Luis, 1998. "Minimal spanning trees with a constraint on the number of leaves," European Journal of Operational Research, Elsevier, vol. 104(1), pages 250-261, January.
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    Cited by:

    1. Francesco Carrabs & Raffaele Cerulli & Ciriaco D’Ambrosio & Federica Laureana, 2021. "The Generalized Minimum Branch Vertices Problem: Properties and Polyhedral Analysis," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 356-377, February.
    2. Mercedes Landete & José Luis Sainz-Pardo, 2022. "The Domatic Partition Problem in Separable Graphs," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    3. 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.

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