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k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut

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Abstract

Given a graph with weights on the edges, a set of origin and destination pairs of nodes, and two integers L ≥ 2 and k ≥ 2, the k-node-disjoint hop-constrained network design problem is to find a minimum weight subgraph of G such that between every origin and destination there exist at least k node-disjoint paths of length at most L. In this paper, we consider this problem from a polyhedral point of view. We propose an integer linear programming formulation for the problem for L ∈{2,3} and arbitrary k, and investigate the associated polytope. We introduce new valid inequalities for the problem for L ∈{2,3,4}, and give necessary and sufficient conditions for these inequalities to be facet defining. We also devise separation algorithms for these inequalities. Using these results, we propose a branch-and-cut algorithm for solving the problem for both L = 3 and L = 4 along with some computational results.

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Acknowledgements

We would like to thank the anonymous referees for their valuable comments that permitted to correct some flaw in the previous version and improve the presentation of the paper.

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Authors and Affiliations

  1. Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, 76600, Le Havre, France

    Ibrahima Diarrassouba

  2. PSL, CNRS UMR 7243 LAMSADE, Université Paris-Dauphine, Place du Maréchal De Lattre de Tassigny, 75775 Cedex 16, Paris, France

    Meriem Mahjoub & A. Ridha Mahjoub

  3. Faculté des Sciences de Tunis, URAPOP, Université Tunis El Manar, UR13ZS38, Tunis, Tunisia

    Meriem Mahjoub

  4. Department of Industrial Engineering, Bilkent University, Bilkent, 06800, Ankara, Turkey

    Hande Yaman

Authors
  1. Ibrahima Diarrassouba
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  2. Meriem Mahjoub
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  3. A. Ridha Mahjoub
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  4. Hande Yaman
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Correspondence to Ibrahima Diarrassouba.

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Diarrassouba, I., Mahjoub, M., Mahjoub, A.R. et al. k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut. Ann. Telecommun. 73, 5–28 (2018). https://doi.org/10.1007/s12243-017-0622-3

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  • DOI: https://doi.org/10.1007/s12243-017-0622-3

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