Survivability in hierarchical telecommunications networks

We consider the problem of designing a two level telecommunications network at minimum cost. The decisions involved are the locations of concentrators, the assignments of user nodes to concentrators and the installation of links connecting concentrators in a reliable backbone network. We define a reliable backbone network as one where there exist at least 2-edge disjoint paths between any pair of concentrator nodes. We formulate this problem as an integer program and propose a facial study of the associated polytope. We describe valid inequalities and give sufficient conditions for these inequalities to be facet defining. We also propose some reduction operations in order to speed up the separation procedures for these inequalities. Using these results, we devise a branch-and-cut algorithm and present some computational results.