A Matroid Generalization of the Super-Stable Matching Problem

TL;DR

This paper extends the concept of super-stable matchings to a matroid framework, introducing super-stable common independent sets and providing a polynomial-time algorithm for their computation.

Contribution

It generalizes super-stable matchings to matroid settings and offers an efficient algorithm for finding super-stable common independent sets.

Findings

Polynomial-time algorithm for super-stable common independent sets

Generalization of super-stable matchings to matroid structures

Extension of previous stable matching algorithms

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.