Non-uniformly Stable Common Independent Sets

TL;DR

This paper introduces a polynomial-time algorithm for checking the existence of non-uniformly stable common independent sets in matroid generalizations of stable matching problems with ties.

Contribution

It proposes a novel polynomial-time algorithm for non-uniform stability in matroid-based stable matching with ties, generalizing super-stability and strong stability.

Findings

Algorithm efficiently checks existence of non-uniformly stable sets

Generalizes previous stability concepts in matroid settings

Advances understanding of stable matchings with ties

Abstract

In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem of checking the existence of a common independent set satisfying non-uniform stability, which is a common generalization of super-stability and strong stability.