Strongly Stable Matchings under Matroid Constraints

TL;DR

This paper addresses the problem of finding strongly stable matchings under matroid constraints with tied preferences, providing a polynomial-time algorithm for existence checking and construction.

Contribution

It introduces the first polynomial-time algorithm for strongly stable matchings under matroid constraints with ties in preferences.

Findings

Polynomial-time algorithm for existence check

Algorithm constructs strongly stable matchings when they exist

Extends stable matching theory to matroid-constrained settings

Abstract

We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference of each agent may contain ties. In this setting, we consider the problem of checking the existence of a strongly stable matching, and finding a strongly stable matching if a strongly stable matching exists. We propose a polynomial-time algorithm for this problem.