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Annals of Telecommunications

, Volume 73, Issue 1–2, pp 5–28 | Cite as

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

  • Ibrahima Diarrassouba
  • Meriem Mahjoub
  • A. Ridha Mahjoub
  • Hande Yaman
Article
  • 147 Downloads

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.

Keywords

k-node-disjoint hop-constrained paths Survivable network Polytope Valid inequalities Facets Separation Branch-and-cut 

Notes

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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Copyright information

© Institut Mines-Télécom and Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Normandie Univ, UNIHAVRE, LMAHLe HavreFrance
  2. 2.PSL, CNRS UMR 7243 LAMSADEUniversité Paris-DauphineParisFrance
  3. 3.Faculté des Sciences de Tunis, URAPOPUniversité Tunis El ManarTunisTunisia
  4. 4.Department of Industrial EngineeringBilkent UniversityBilkentTurkey

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