k-node-disjoint hop-constrained survivable networks: polyhedral analysis and branch and cut
Author
Diarrassouba, I.
Mahjoub, M.
Mahjoub, A. R.
Yaman, H.
Date
2018Source 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
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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-cutFacets
K-node-disjoint hop-constrained paths
Polytope
Separation
Survivable network
Valid inequalities