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Minimum spanning tree with conflicting edge pairs: a branch-and-cut approach

Author

Listed:
  • Francesco Carrabs

    (University of Salerno)

  • Raffaele Cerulli

    (University of Salerno)

  • Rosa Pentangelo

    (University of Salerno)

  • Andrea Raiconi

    (University of Salerno)

Abstract

In this paper, we show a branch-and-cut approach to solve the minimum spanning tree problem with conflicting edge pairs. This is a NP-hard variant of the classical minimum spanning tree problem, in which there are mutually exclusive edges. We introduce a new set of valid inequalities for the problem, based on the properties of its feasible solutions, and we develop a branch-and-cut algorithm based on them. Computational tests are performed both on benchmark instances coming from the literature and on some newly proposed ones. Results show that our approach outperforms a previous branch-and-cut algorithm proposed for the same problem.

Suggested Citation

  • Francesco Carrabs & Raffaele Cerulli & Rosa Pentangelo & Andrea Raiconi, 2021. "Minimum spanning tree with conflicting edge pairs: a branch-and-cut approach," Annals of Operations Research, Springer, vol. 298(1), pages 65-78, March.
    • Handle: RePEc:spr:annopr:v:298:y:2021:i:1:d:10.1007_s10479-018-2895-y
    DOI: 10.1007/s10479-018-2895-y
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    References listed on IDEAS

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    1. Ulrich Pferschy & Joachim Schauer, 2013. "The maximum flow problem with disjunctive constraints," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 109-119, July.
    2. Ruslan Sadykov & François Vanderbeck, 2013. "Bin Packing with Conflicts: A Generic Branch-and-Price Algorithm," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 244-255, May.
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    Cited by:

    1. Chou, Xiaochen & Dell’Amico, Mauro & Jamal, Jafar & Montemanni, Roberto, 2023. "Precedence-Constrained arborescences," European Journal of Operational Research, Elsevier, vol. 307(2), pages 575-589.
    2. 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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