# Finding Robust Solutions to Stable Marriage

## TL;DR

This paper introduces a new robustness concept for stable matchings, defines the most robust stable matching, and compares algorithms to find it, with local search performing best on large instances.

## Contribution

It defines (a,b)-supermatches for robustness in stable matchings and develops algorithms including local search to efficiently find the most robust solution.

## Key findings

- Local search outperforms other methods on large instances.
- Checking robustness as a (1,b)-supermatch is polynomial-time solvable.
- The approach effectively identifies highly robust stable matchings.

## Abstract

We study the notion of robustness in stable matching problems. We first define robustness by introducing (a,b)-supermatches. An $(a,b)$-supermatch is a stable matching in which if $a$ pairs break up it is possible to find another stable matching by changing the partners of those $a$ pairs and at most $b$ other pairs. In this context, we define the most robust stable matching as a $(1,b)$-supermatch where b is minimum. We show that checking whether a given stable matching is a $(1,b)$-supermatch can be done in polynomial time. Next, we use this procedure to design a constraint programming model, a local search approach, and a genetic algorithm to find the most robust stable matching. Our empirical evaluation on large instances show that local search outperforms the other approaches.