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New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller-Tucker-Zemlin constraints

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  • Akgün, Ibrahim
  • Tansel, Barbaros Ç.

Abstract

Given an undirected network with positive edge costs and a natural number p, the Hop-Constrained Minimum Spanning Tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, we develop new formulations for HMST. The formulations are based on Miller-Tucker-Zemlin (MTZ) subtour elimination constraints, MTZ-based liftings in the literature offered for HMST, and a new set of topology-enforcing constraints. We also compare the proposed models with the MTZ-based models in the literature with respect to linear programming relaxation bounds and solution times. The results indicate that the new models give considerably better bounds and solution times than their counterparts in the literature and that the new set of constraints is competitive with liftings to MTZ constraints, some of which are based on well-known, strong liftings of Desrochers and Laporte (1991).

Suggested Citation

  • Akgün, Ibrahim & Tansel, Barbaros Ç., 2011. "New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller-Tucker-Zemlin constraints," European Journal of Operational Research, Elsevier, vol. 212(2), pages 263-276, July.
    • Handle: RePEc:eee:ejores:v:212:y:2011:i:2:p:263-276
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    References listed on IDEAS

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    1. Gouveia, Luis, 1996. "Multicommodity flow models for spanning trees with hop constraints," European Journal of Operational Research, Elsevier, vol. 95(1), pages 178-190, November.
    2. Hanif D. Sherali & Patrick J. Driscoll, 2002. "On Tightening the Relaxations of Miller-Tucker-Zemlin Formulations for Asymmetric Traveling Salesman Problems," Operations Research, INFORMS, vol. 50(4), pages 656-669, August.
    3. Gouveia, Luis & Pires, Jose Manuel, 1999. "The asymmetric travelling salesman problem and a reformulation of the Miller-Tucker-Zemlin constraints," European Journal of Operational Research, Elsevier, vol. 112(1), pages 134-146, January.
    4. Luis Gouveia, 1998. "Using Variable Redefinition for Computing Lower Bounds for Minimum Spanning and Steiner Trees with Hop Constraints," INFORMS Journal on Computing, INFORMS, vol. 10(2), pages 180-188, May.
    5. Pirkul, Hasan & Soni, Samit, 2003. "New formulations and solution procedures for the hop constrained network design problem," European Journal of Operational Research, Elsevier, vol. 148(1), pages 126-140, July.
    6. Larry J. LeBlanc & Jerome Chifflet & Philippe Mahey, 1999. "Packet Routing in Telecommunication Networks with Path and Flow Restrictions," INFORMS Journal on Computing, INFORMS, vol. 11(2), pages 188-197, May.
    7. Anantaram Balakrishnan & Kemal Altinkemer, 1992. "Using a Hop-Constrained Model to Generate Alternative Communication Network Design," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 192-205, May.
    8. 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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    Cited by:

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    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.

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