Single commodity-flow algorithms for lifts of graphic and co-graphic matroids

Authors:
Bertrand Guenin;Leanne Stuive
Affiliations:
Dept. of Combinatorics & Optimization, Faculty of Mathematics, University of Waterloo, Canada;Dept. of Combinatorics & Optimization, Faculty of Mathematics, University of Waterloo, Canada
Venue:
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Year:
2013

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Abstract

Consider a binary matroid M given by its matrix representation. We show that if M is a lift of a graphic or a co-graphic matroid, then in polynomial time we can either solve the single commodity flow problem for M or find an obstruction for which the Max-Flow Min-Cut relation does not hold. The key tool is an algorithmic version of Lehman's Theorem for the set covering polyhedron.