Modeling Stable Matching Problems with Answer Set Programming

TL;DR

This paper presents an Answer Set Programming encoding for the Stable Marriage Problem that is flexible, easily extendable, and capable of finding optimal stable matchings under various conditions.

Contribution

It introduces a versatile ASP-based encoding for SMP that simplifies adapting to different variants and enables selecting optimal solutions with existing solvers.

Findings

The encoding handles preferences with unacceptable partners.

It supports ties in preferences.

It can find optimal stable matchings based on specific criteria.

Abstract

The Stable Marriage Problem (SMP) is a well-known matching problem first introduced and solved by Gale and Shapley (1962). Several variants and extensions to this problem have since been investigated to cover a wider set of applications. Each time a new variant is considered, however, a new algorithm needs to be developed and implemented. As an alternative, in this paper we propose an encoding of the SMP using Answer Set Programming (ASP). Our encoding can easily be extended and adapted to the needs of specific applications. As an illustration we show how stable matchings can be found when individuals may designate unacceptable partners and ties between preferences are allowed. Subsequently, we show how our ASP based encoding naturally allows us to select specific stable matchings which are optimal according to a given criterion. Each time, we can rely on generic and efficient off-the-shelf answer set solvers to find (optimal) stable matchings.