Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints

In this paper a general integer linear programming model is presented for the important practical problem of designing minimum-cost survivable networks, and this model is related to concepts in graph theory and polyhedral combinatorics. In particular, several interesting special cases of this general model are considered, including the minimum spanning tree problem, the Steiner tree problem, and the minimum cost k-edge connected and k-node connected network design problems. The integer polyhedra associated with these problems are studied, those inequalities from natural ILP-formulations that define facets are identified, the separation problem for these facets is addressed, and how good lower bounds can be obtained from the models studied here is indicated.