Design of survivable networks with low connectivity requirements

In this paper, we consider the survivable network design problem when the connectivity types are in {0, 1, 2, 3}. The problem has wide applications in telecommunication networks. We consider the problem from a polyhedral point of view. We describe several classes of valid inequalities and give necessary conditions and sufficient conditions for these inequalities to be facet defining. We also develop separation routines for these inequalities. Using these results, we devise a branch‐and‐cut algorithm along with an extensive computational study is presented.