A MATROID GENERALIZATION OF THE SUPER-STABLE MATCHING PROBLEM

A super-stable matching is a solution concept in the variant of the stable matching problem in which the preferences may contain ties. Irving proposed a polynomial-time algorithm for the problem of checking the existence of a super-stable matching and finding a super-stable matching if a super-stable matching exists. In this paper, we consider a matroid generalization of a super-stable matching. We call our generalization of a super-stable matching a super-stable common independent set. This can be considered as a generalization of the matroid generalization of a stable matching for strict preferences proposed by Fleiner. We propose a polynomial-time algorithm for the problem of checking the existence of a super-stable common independent set and finding a super-stable common independent set if a super-stable common independent set exists. © 2022 Society for Industrial and Applied Mathematics.