A GOOD ALGORITHM FOR LEXICOGRAPHICALLY OPTIMAL FLOWS IN MULTI-TERMINAL NETWORKS

Let a network have several sources and sinks. For any flow f let of and rf denote the vectors of net flows out of the sources and into the sinks, respectively, arranged in order of increasing magnitude. Our algorithm computes an f for which both of and rf are lexicographic maxima. For a net- work with n nodes this algorithm terminates within 0(nS) operations.