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Given a weighted undirected graph G with a set of pairs of terminals {s i , t i }, i = 1, ..., d, and an integer L ≥ 2, the two node-disjoint hop-constrained sur-vivable network design problem (TNHNDP) is to find a minimum weight subgraph of G such that between every s i and t i there exist at least two node-disjoint paths of length at most L. This problem(More)
In this paper we describe a Branch-and-Cut algorithm for the k-edge connected subgraph problem. This problem has applications in the design of survivable telecommunication networks. We introduce a new family of valid inequalities for the associated polytope. We give sufficient conditions for these inequalities to be facet defining and devise separation(More)
In this paper, we study the k edge-connected L-hop-constrained network design problem. Given a weighted graph G = (V, E), a set D of pairs of nodes, two integers L ≥ 2 and k ≥ 2, the problem consists in finding a minimum weight subgraph of G containing at least k edge-disjoint paths of length at most L between every pairs {s, t} ∈ D. We consider the problem(More)
In this paper we consider the k-node-connected subgraph problem. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We introduce further classes of valid inequalities and discuss their facial aspect. We also devise separation routines and discuss some structure properties and reduction operations.(More)
The survivable k-node-connected network design problem : Valid inequialities and Branch-and-Cut. Abstract In this paper we consider the k-node-connected subgraph problem. We propose an integer linear programming formulation for the problem and investigate the associated polytope. We introduce further classes of valid inequalities and discuss their facial(More)
Network design problems have been largely studied in the last decades due to the ubiquity of IT communication in our daily life. We address in this paper the k-edge-connected hop-constrained network design problem (kHNDP) which is known to be NP-hard. In this paper, we present a hybrid parallel approach for solving the kHNDP based on a Lagrangian relaxation(More)