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

Abstract

Given a graph G=( V, E) with edge costs and an integer vector r∈ Z + V associated with the nodes of V, the survivable 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∈{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.