The k edge-disjoint 3-hop-constrained paths polytope
Bendali, Fatiha; Mahjoub, Ali Ridha; Mailfert, Jean; Diarrassouba, Ibrahima (2010), The k edge-disjoint 3-hop-constrained paths polytope, Discrete Optimization, 7, 4, p. 222-233. http://dx.doi.org/10.1016/j.disopt.2010.05.001
TypeArticle accepté pour publication ou publié
Journal nameDiscrete Optimization
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Abstract (EN)Given a graph G with two distinguished nodes s and t, a cost on each edge of G and two fixed integers k≥2, L≥2, the k edge-disjoint L-hop-constrained paths problem is to find a minimum cost subgraph of G such that between s and t there are at least k edge-disjoint paths of length at most L. In this paper we consider this problem from a polyhedral point of view. We give an integer programming formulation for the problem and discuss the associated polytope. In particular, we show that when L=3 and k≥2, the linear relaxation of the associated polytope, given by the trivial, the st-cut and the so-called L-path-cut inequalities, is integral. As a consequence, we obtain a polynomial time cutting plane algorithm for the problem when L=2,3 and k≥1. This generalizes the results of Huygens et al. (2004)  for k=2 and L=2,3 and those of Dahl et al. (2006)  for L=2 and k≥2. This also proves a conjecture in .
Subjects / KeywordsSurvivable network; Edge-disjoint paths; Hop-constrained paths; Flow; Polytope; Facet
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