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The k edge-disjoint 3-hop-constrained paths polytope

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Date
2010
Dewey
Principes généraux des mathématiques
Sujet
Survivable network; Edge-disjoint paths; Hop-constrained paths; Flow; Polytope; Facet
Journal issue
Discrete Optimization
Volume
7
Number
4
Publication date
2010
Article pages
222-233
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.disopt.2010.05.001
URI
https://basepub.dauphine.fr/handle/123456789/5806
Collections
  • LAMSADE : Publications
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Author
Bendali, Fatiha
Mahjoub, Ali Ridha
Mailfert, Jean
Diarrassouba, Ibrahima
Type
Article accepté pour publication ou publié
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) [1] for k=2 and L=2,3 and those of Dahl et al. (2006) [2] for L=2 and k≥2. This also proves a conjecture in [1].

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