Matroid Matching: the Power of Local Search

Copyright © [2013] by The Society for Industrial and Applied Mathematics. All rights reserved

We consider the classical matroid matching problem. Unweighted matroid matching for linear matroids was solved by Lovasz, and the problem is known to be intractable for general matroids. We present a PTAS for unweighted matroid matching for general matroids. In contrast, we show that natural LP relaxations that have been studied have an (n) integrality gap and moreover, (n) rounds of the Sherali-Adams hierarchy are necessary to bring the gap down to a constant.

More generally, for any fixed and , we obtain a ()-approximation for matroid matching in k-uniform hypergraphs, also known as the matroid k-parity problem. As a consequence, we obtain a ()-approximation for the problem of finding the maximum-cardinality set in the intersection of k matroids. We also design a 3/2-approximation for the weighted version of a known special case of matroid matching, the matchoid problem.

By: Jon Lee; Maxim Sviridenko; Jan Vondrák

Published in: SIAM Journal on Computing, volume 42, (no 1), pages 357-79 in 2013


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