A linear programming formulation of Mader's edge-disjoint paths problem

Authors:
J. C. M. Keijsper;R. A. Pendavingh;L. Stougie
Affiliations:
Technische Universiteit Eindhoven, Department of Mathematics and Computer Science, MB Eindhoven, Netherlands;Technische Universiteit Eindhoven, Department of Mathematics and Computer Science, MB Eindhoven, Netherlands;Technische Universiteit Eindhoven, Department of Mathematics and Computer Science, MB Eindhoven, Netherlands and CWI in Amsterdam
Venue:
Journal of Combinatorial Theory Series B
Year:
2006

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Abstract

We give a dual pair of linear programs for a min-max result of Mader describing the maximum number of edge-disjoint T-paths in a graph G = (V, E) with T ⊆ V. We conclude that there exists a polynomial-time algorithm (based on the ellipsoid method) for finding the maximum number of T- paths in a capacitated graph, where the number of T-paths using an edge does not exceed the capacity of that edge.