The survivable hierarchical telecommunications network design problem consists of locating concentrators, assigning user nodes to concentrators, and linking concentrators in a reliable backbone network. In this article, we study this problem when the backbone is 2-edge connected and when user nodes are linked to concentrators by a point-to-point access network. We formulate this problem as an integer linear program and present a facial study of the associated polytope. We describe valid inequalities and give sufficient conditions for these inequalities to be facet defining. We investigate the computational complexity of the corresponding separation problems. We propose some reduction operations to speed up the separation procedures. Finally, we devise a branch-and-cut algorithm based on these results and present the outcome of a computational study.

T he motivation behind this study is the essential need for survivability in the telecommunications networks.An optical signal should find its destination even if the network experiences an occasional fiber cut. We consider the design of a two-level survivable telecommunications network. Terminals compiling the access layer communicate through hubs forming the backbone layer. To hedge against single link failures in the network, we require the backbone subgraph to be two-edge connected and the terminal nodes to connect to the backbone layer in a dual-homed fashion, i.e., at two distinct hubs. The underlying design problem partitions a given set of nodes into hubs and terminals, chooses a set of connections between the hubs such that the resulting backbone network is two-edge connected, and for each terminal chooses two hubs to provide the dual-homing backbone access. All of these decisions are jointly made based on some cost considerations. We give alternative formulations using cut inequalities, compare these formulations, provide a polyhedral analysis of the smallsized formulation, describe valid inequalities, study the associated separation problems, and design variable fixing rules. All of these findings are then utilized in devising an efficient branch-and-cut algorithm to solve this network design problem.