Solving minimum-cost shared arborescence problems

In this work the minimum-cost shared network problem (MCSN) is introduced, where the objective is to find a minimum-cost subgraph, which is shared among multiple entities such that each entity is able to fulfil its own set of topological constraints. The topological constraints may induce structures like Steiner trees, minimum spanning trees, shortest paths, etc. The cost function to be minimized is a combination of the costs for the shared network and the costs incurred by each entity. The minimum cost shared Steiner arborescence problem (SStA) is a special case of the MCSN, in which the underlying structures take the form of Steiner trees. The SStA has been used in the literature to establish shared functional modules in protein interaction networks. A cut formulation for the SStA and Benders decomposition thereof are proposed in this article and computationally evaluated and compared with a previously proposed flow-based formulation. The effectiveness of the algorithms is illustrated on two types of instances derived from protein-interaction networks (available from the previous literature) and from telecommunication access networks.