An n-ary Constraint for the Stable Marriage Problem

TL;DR

This paper introduces an efficient n-ary constraint for the stable marriage problem that enforces stability and disallows bigamy, offering faster and more space-efficient solutions compared to previous encodings.

Contribution

It presents a novel n-ary constraint for the stable marriage problem that simplifies enforcement and improves computational efficiency.

Findings

Enforces stability with a single constraint for n men and women

Achieves $O(n^2)$ complexity in enforcing arc-consistency

Outperforms previous encodings in speed and space efficiency

Abstract

We present an n-ary constraint for the stable marriage problem. This constraint acts between two sets of integer variables where the domains of those variables represent preferences. Our constraint enforces stability and disallows bigamy. For a stable marriage instance with $n$ men and $n$ women we require only one of these constraints, and the complexity of enforcing arc-consistency is $O(n^2)$ which is optimal in the size of input. Our computational studies show that our n-ary constraint is significantly faster and more space efficient than the encodings presented in \cite{cp01}. We also introduce a new problem to the constraint community, the sex-equal stable marriage problem.