Strong Formulations for 2-Node-Connected Steiner Network Problems

We consider a survivable network design problem known as the 2-NodeConnected Steiner Network Problem (2NCON): we are given a weighted undirected graph with a node partition into two sets of customer nodes and one set of Steiner nodes. We ask for the minimum weight connected subgraph containing all customer nodes, in which the nodes of the second customer set are nodewise 2-connected. This problem class has received lively attention in the past, especially with regard to exact ILP formulations and their polyhedral properties. In this paper, we present a transformation of this problem into a related problem considering directed graphs and use this to establish two novel ILP formulations to solve 2NCON, based on multi-commodity flow and on directed cuts, respectively. We prove the advantages of our formulations and compare both approaches theoretically as well as experimentally. Thereby we solve instances with up to 1600 nodes to provable optimality.