SOLVING INTEGER MINIMUM COST FLOWS WITH SEPARABLE CONVEX COST OBJECTIVE POLYNOMIALLY.

Abstract

A polynomial algorithm is described to solve minimum cost network flow problems with separable convex cost functions on the arcs and integrality restrictions on the flows. The proof generalizes the scaling approach used by J. Edmonds and R. M. Karp for proving polynomiality of the out-of-killer method for ordinary (linear cost) network flows.