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Hop constrained Steiner trees with multiple root nodes

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  • Gouveia, Luis
  • Leitner, Markus
  • Ljubić, Ivana

Abstract

We consider a network design problem that generalizes the hop and diameter constrained Steiner tree problem as follows: Given an edge-weighted undirected graph with two disjoint subsets representing roots and terminals, find a minimum-weight subtree that spans all the roots and terminals so that the number of hops between each relevant node and an arbitrary root does not exceed a given hop limit H. The set of relevant nodes may be equal to the set of terminals, or to the union of terminals and root nodes. This article proposes integer linear programming models utilizing one layered graph for each root node. Different possibilities to relate solutions on each of the layered graphs as well as additional strengthening inequalities are then discussed. Furthermore, theoretical comparisons between these models and to previously proposed flow- and path-based formulations are given. To solve the problem to optimality, we implement branch-and-cut algorithms for the layered graph formulations. Our computational study shows their clear advantages over previously existing approaches.

Suggested Citation

  • Gouveia, Luis & Leitner, Markus & Ljubić, Ivana, 2014. "Hop constrained Steiner trees with multiple root nodes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 100-112.
    • Handle: RePEc:eee:ejores:v:236:y:2014:i:1:p:100-112
    DOI: 10.1016/j.ejor.2013.11.029
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    References listed on IDEAS

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    1. S. Voß, 1999. "The Steiner tree problem with hop constraints," Annals of Operations Research, Springer, vol. 86(0), pages 321-345, January.
    2. Luis Gouveia & Thomas Magnanti & Cristina Requejo, 2006. "An intersecting tree model for odd-diameter-constrained minimum spanning and Steiner trees," Annals of Operations Research, Springer, vol. 146(1), pages 19-39, September.
    3. Gouveia, Luis & Requejo, Cristina, 2001. "A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 132(3), pages 539-552, August.
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    Citations

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    Cited by:

    1. Gustavo Bergantiños & Leticia Lorenzo, 2021. "Cost additive rules in minimum cost spanning tree problems with multiple sources," Annals of Operations Research, Springer, vol. 301(1), pages 5-15, June.
    2. Gustavo Bergantiños & Youngsub Chun & Eunju Lee & Leticia Lorenzo, 2022. "The Folk Rule for Minimum Cost Spanning Tree Problems with Multiple Sources," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 24(01), pages 1-36, March.
    3. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    4. Leitner, Markus & Ljubić, Ivana & Riedler, Martin & Ruthmair, Mario, 2020. "Exact approaches for the directed network design problem with relays," Omega, Elsevier, vol. 91(C).
    5. De Boeck, Jérôme & Fortz, Bernard, 2018. "Extended formulation for hop constrained distribution network configuration problems," European Journal of Operational Research, Elsevier, vol. 265(2), pages 488-502.
    6. Gouveia, Luis & Leitner, Markus & Ruthmair, Mario, 2017. "Extended formulations and branch-and-cut algorithms for the Black-and-White Traveling Salesman Problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 908-928.

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