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      • Department of Industrial Engineering
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      k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut

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      Author
      Diarrassouba, I.
      Mahjoub, M.
      Mahjoub, A. R.
      Yaman, H.
      Date
      2018
      Source Title
      Annales des Telecommunications/Annals of Telecommunications
      Print ISSN
      0003-4347
      Publisher
      Springer-Verlag France
      Volume
      73
      Issue
      1-2
      Pages
      5 - 28
      Language
      English
      Type
      Article
      Item Usage Stats
      128
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      486
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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.
      Keywords
      Branch-and-cut
      Facets
      K-node-disjoint hop-constrained paths
      Polytope
      Separation
      Survivable network
      Valid inequalities
      Permalink
      http://hdl.handle.net/11693/49820
      Published Version (Please cite this version)
      https://doi.org/10.1007/s12243-017-0622-3
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      • Department of Industrial Engineering 694
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