MATROID INTERSECTION WITH PRIORITY CONSTRAINTS

Naoyuki Kamiyama
2013 Journal of the Operations Research Society of Japan  
In this paper, we consider the fo11owing variant of the matroid intersection problem. We are given two matroids Mi, M2 on the same ground set E and a subset A of E, Our goal is to find a common independent set I of Mi, M2 such that 1Jn AI is maximum among all common independent sets of Mi, M2 and such that (secondly) III is maximum arnong all common independent sets of Mi,M2 satisfying the first cendition. This problem is a matroid-geoeralization of the simplest case of the rank-maximal
more » ... problem introduced by Irving, Karritha, Mehlhorn, Michail and Paluch (2006). In this paper, we extend the "combinatorial" algorithm of lrving et al, for the rank-maximal matching problem to our problem by using a DulmageMendelsehn type decomposition for the matroid intersection problem.
doi:10.15807/jorsj.56.15 fatcat:rsfm7fxh4bhmznsgnvtqh6ttqy