Local search for stable marriage problems with ties and incomplete lists

TL;DR

This paper introduces a local search method to efficiently find large stable matchings in the stable marriage problem with ties and incomplete lists, addressing an NP-hard optimization challenge.

Contribution

It presents a novel local search approach tailored for the stable marriage problem with ties and incomplete lists, enabling large-scale solutions efficiently.

Findings

Successfully solves large problem instances quickly

Achieves large and often optimal stable matchings

Reduces neighborhood size for efficient local moves

Abstract

The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the stable marriage problem, where the men and women express their preferences using a preference list with ties over a subset of the members of the other sex. Matchings are permitted only with people who appear in these preference lists. In this setting, we study the problem of finding a stable matching that marries as many people as possible. Stability is an envy-free notion: no man and woman who are not married to each other would both prefer each other to their partners or to being single. This problem is NP-hard. We tackle this problem using local search, exploiting properties of the problem to reduce the size of the neighborhood and to make local moves efficiently. Experimental results show that this approach is able to solve large problems, quickly returning stable matchings of large and often optimal size.