A New ILP Formulation for 2-Root-Connected Prize-Collecting Steiner Networks

We consider the real-world problem of extending a given infrastructure network in order to connect new customers. By representing the infrastructure by a single root node, this problem can be formulated as a 2-root-connected prize-collecting Steiner network problem in which certain customer nodes require two node-disjoint paths to the root, and other customers only a simple path. Herein, we present a novel ILP approach to solve this problem to optimality based on directed cuts. This formulation becomes possible by exploiting a certain orientability of the given graph. To our knowledge, this is the first time that such an argument is used for a problem with node-disjointness constraints. We prove that this formulation is stronger than the well-known undirected cut approach. Our experiments show its efficiency over the other formulations presented for this problem, i.e., the undirected cut approach and a formulation based on multi-commodity flow.