In this paper we give a flow model on directed multigraphs by introducing  reflexions of generalized polymatroids at vertices as constraints for the flow  conservation. This model has the essential features of the classical flow model, primarily  the max-flow min-cut theorem and the polynomial algorithm for computing  the maximal feasible (integral) flow

M. Kochol

. In this paper we give a flow model on directed multigraphs by introducing reflexions of generalized polymatroids at vertices as constraints for the flow conservation. This model has the essential features of the classical flow model, primarily the max-flow min-cut theorem and the polynomial algorithm for computing the maximal feasible (integral) flow. 1. Introduction  Since the classical network flow model of Ford and Fulkerson appeared in the 1950&apos;s, numerous generalizations and variations of this model have been introduced. Very interesting is the polymatroidal network flow model introduced by Lawler and Martel [12] and Hassin [9] which provides a generalization and unification of both network flow theory and much of the theory of polymatroid optimization (see [13]). Note that (integral) polymatroids are polyhedra of nonnegative vectors bounded by (integral) submodular function. They have been introduced by Edmonds [2] as generalizations of matroids. (Integral) polymatroids and the..

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Quasi Polymatroidal Flow Networks

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Quasi Polymatroidal Flow Networks

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