Solving stable matching problems using answer set programming

TL;DR

This paper presents an answer set programming approach to solve various stable matching problems, including complex variants with ties and unacceptable partners, offering a flexible and efficient exact solution.

Contribution

It introduces the first ASP encoding capable of finding optimal stable matchings with complex preferences and constraints, adaptable to diverse application needs.

Findings

Efficient ASP encoding for stable matchings with ties and unacceptable partners

Ability to select optimal matchings based on user-defined criteria

First exact implementation for complex stable matching variants

Abstract

Since the introduction of the stable marriage problem (SMP) by Gale and Shapley (1962), several variants and extensions have been investigated. While this variety is useful to widen the application potential, each variant requires a new algorithm for finding the stable matchings. To address this issue, we propose an encoding of the SMP using answer set programming (ASP), which can straightforwardly be adapted and extended to suit the needs of specific applications. The use of ASP also means that we can take advantage of highly efficient off-the-shelf solvers. To illustrate the flexibility of our approach, we show how our ASP encoding naturally allows us to select optimal stable matchings, i.e. matchings that are optimal according to some user-specified criterion. To the best of our knowledge, our encoding offers the first exact implementation to find sex-equal, minimum regret, egalitarian or maximum cardinality stable matchings for SMP instances in which individuals may designate unacceptable partners and ties between preferences are allowed. This paper is under consideration in Theory and Practice of Logic Programming (TPLP).