Matroid Intersection with Priority Constraints
نویسنده
چکیده
In this paper, we consider the following variant of the matroid intersection problem. We are given two matroids M1,M2 on the same ground set E and a subset A of E. Our goal is to find a common independent set I of M1,M2 such that |I ∩A| is maximum among all common independent sets of M1,M2 and such that (secondly) |I| is maximum among all common independent sets of M1,M2 satisfying the first condition. This problem is a matroid-generalization of the simplest case of the rank-maximal matching problem introduced by Irving, Kavitha, Mehlhorn, Michail and Paluch (2006). In this paper, we extend the “combinatorial” algorithm of Irving et al. for the rank-maximal matching problem to our problem by using a Dulmage-Mendelsohn type decomposition for the matroid intersection problem.
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