A Matroid Generalization of the Super-Stable Matching Problem
Abstract
A super-stable matching, which was introduced by Irving, is a solution concept in a variant of the stable matching problem in which the preferences may contain ties. Irving proposed a polynomial-time algorithm for the problem of 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 finding a super-stable common independent set if a super-stable common independent set exists.
Cite
@article{arxiv.2010.03820,
title = {A Matroid Generalization of the Super-Stable Matching Problem},
author = {Naoyuki Kamiyama},
journal= {arXiv preprint arXiv:2010.03820},
year = {2022}
}
Comments
v2: small mistakes and typos are fixed, and proofs are improved