An efficient generic network flow constraint

Abstract

We propose a generic global constraint that can be applied to model a wide range of network flow problems using constraint programming. In our approach, all key aspects of a network flow can be represented by finite domain variables, making the constraint very expressive. At the same time, we utilize a network simplex algorithm to design a highly efficient, and incremental, domain filtering algorithm. We thus integrate two powerful techniques for discrete optimization: constraint programming and the network simplex algorithm. Our generic constraint can be applied to automatically implement effective and efficient domain filterng algorithms for ad-hoc networks, but also for existing global constraints that rely on a network structure, including several soft global constraints many of which are not yet supported by CP systems. Our experimental results demonstrate the efficiency of our constraint, that can achieve speed-ups of several orders of magnitude with negligible overhead, when compared to a decomposition into primitive constraints.