On fractional multicommodity flows and distance functions

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...

Multicommodity Flows and Column Generation

Multicommodity Flows Handout

Stable Multicommodity Flows

We extend the stable flow model of Fleiner to multicommodity flows. In addition to the preference lists of agents on trading partners for each commodity, every trading pair has a preference list on the commodities that the seller can sell to the buyer. A blocking walk (with respect to a certain commodity) may include saturated arcs, provided that a positive amount of less preferred commodity is...