MULTICOMMODITY NETWORK FLOWS WITH NONCONVEX ARC COSTS

Shortest Paths and Multicommodity Network Flows

Integer Multicommodity Flows with Reduced

Given a supply graph G = (V; E), a demand graph H = (T; D), edge capacities c : E 7 ! II N and requests r : D 7 ! II N, we consider the problem of nding integer multiiows subject to c; r. Korach and Penn constructed approximate integer multiiows for planar graphs, but no results were known for the general case. Via derandomization we present a polynomial-time approximation algorithm. There are ...

Integer Multicommodity Flows with Reduced Demands Integer Multicommodity Flows with Reduced Demands

Given a supply graph G = (V; E), a demand graph H = (T; D), edge capacities c : E 7 ! II N and requests r : D 7 ! II N, we consider the problem of nding integer multiiows subject to c; r. Korach and Penn constructed approximate integer multiiows for planar graphs, but no results were known for the general case. Via derandomization we present a polynomial-time approximation algorithm. There are ...

Multicommodity Flows and Polyhedra

Seymour s conjecture on binary clutters with the so called weak or Q max ow min cut property implies if true a wide variety of results in combinatorial optimization about objects ranging from matchings to mul ticommodity ows and disjoint paths In this paper we review in particular the relation between classes of multicommodity ow problems for which the so called cut condition is su cient and cl...

Criticality for multicommodity flows

For k ≥ 1, the k-commodity flow problem is, we are given k pairs of vertices in a graph G, and we ask whether there exist k flows in the graph, where • the ith flow is between the ith pair of vertices, and has total value one; and • for each edge e, the sum of absolute values of the flows along e is at most one. We prove that for all k there exists n(k) such that if G is connected, and contract...