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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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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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