Separation of partition inequalities for the (1,2)-survivable network design problem

Given a graph G = (V, E) with edge costs and an integer vector r is an element of Z(+)(V) associated with network design problem is to find a minimum cost subgraph of G such that between every pair of nodes s, t of V, there are at least min{r(s), r(t)} edge-disjoint paths. In this paper we consider that problem when r is an element of {1, 2}(V). This case is of particular interest to the telecommunication industry. We show that the separation problem for the so-called partition inequalities reduces to minimizing a submodular function. This yields a polynomial time separation algorithm for these inequalities in that case. (C) 2002 Elsevier Science B.V. All rights reserved.