BibTeX
@MISC{Kamiyama13matroidintersection,
author = {Naoyuki Kamiyama},
title = {MATROID INTERSECTION WITH PRIORITY CONSTRAINTS },
year = {2013}
}
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Abstract
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 ofM1,M2 such that |I ∩A | is maximum among all common independent sets ofM1,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.
