An Introduction to Polymatroidal Network Flows

Abstract

In the “classical” network flow model, flows are constrained by the capacities of individual arcs. In the “polymatroidal” network flow model, flows are constrained by the capacities of sets of arcs. Yet the essential features of the classical model are retained: the augmenting path theorem, the integral flow theorem, and the max-flow min-cut theorem all yield to straightforward generalization. In this paper we provide an introduction to the theory of polymatroidal network flows, with the objective of showing that this theory provides a satisfying generalization and unification of both classical network flow theory and much of the theory of matroid optimization.