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arXiv · 0806.1818

An algorithm for weighted fractional matroid matching

Dion Gijswijt·Gyula Pap
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Abstract

Let M be a matroid on ground set E. A subset l of E is called a `line' when its rank equals 1 or 2. Given a set L of lines, a `fractional matching' in (M,L) is a nonnegative vector x indexed by the lines in L, that satisfies a system of linear constraints, one for each flat of M. Fractional matchings were introduced by Vande Vate, who showed that the set of fractional matchings is a half-integer relaxation of the matroid matching polytope. It was shown by Chang et al. that a maximum size fractional matching can be found in polynomial time. In this paper we give a polynomial time algorithm to find for any given weights on the lines in L, a maximum weight fractional matching.

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Dion Gijswijt, Gyula Pap. 2008-06-11. An algorithm for weighted fractional matroid matching. https://doi.org/10.1016/j.jctb.2013.05.004

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