Two Node-Disjoint Hop-Constrained Survivable Network Design and Polyhedra

Ibrahima Diarrassoubaa (1) , Hakan Kutucu (2) , Ridha Mahjoub (3)

1 ULH - Université Le Havre Normandie
2 Department of Mathematics, Izmir Institute of Technology,
3 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

Given a weighted undirected graph G with a set of pairs of terminals {si, ti}, i = 1, ..., d, and an integer L ≥ 2, the two node-disjoint hop-constrained survivable network design problem (TNHNDP) is to find a minimum weight subgraph of G such that between every si and ti there exist at least two node-disjoint paths of length at most L. This problem has applications to the design of survivable telecommunications networks with QoS-constraints. We discuss this problem from a polyhedral point of view. We present several classes of valid inequalities along with necessary and/or sufficient conditions for these inequalities to be facet defining. We also discuss separation routines for these classes of inequalities. Using this, we propose a Branch-and-Cut algorithm for the problem when L = 3, and present some computational results.

Mots clés: Survivable network; node-disjoint paths; hop constraint; polyhedron; facet; branch and cut

Domaines: Recherche opérationnelle [math.OC]; Ingénierie, finance et science [cs.CE]

Ibrahima Diarrassoubaa, Hakan Kutucu, Ridha Mahjoub. Two Node-Disjoint Hop-Constrained Survivable Network Design and Polyhedra. 2013. ⟨hal-00874354⟩