Stable Marriage Problems with Ties and Incomplete Preferences: An Empirical Comparison of ASP, SAT, ILP, CP, and Local Search Methods

TL;DR

This paper empirically compares various computational methods including ASP, SAT, ILP, CP, and Local Search for solving the SMTI problem, which involves preferences with ties and incompleteness, across three optimization variants.

Contribution

It provides a comprehensive empirical evaluation of multiple solving techniques for SMTI, highlighting their relative performance and effectiveness.

Findings

ASP outperforms SAT in SMTI instances

Local Search is effective for Max Cardinality variants

ILP and CP show competitive results across variants

Abstract

We study a variation of the Stable Marriage problem, where every man and every woman express their preferences as preference lists which may be incomplete and contain ties. This problem is called the Stable Marriage problem with Ties and Incomplete preferences (SMTI). We consider three optimization variants of SMTI, Max Cardinality, Sex-Equal and Egalitarian, and empirically compare the following methods to solve them: Answer Set Programming, Constraint Programming, Integer Linear Programming. For Max Cardinality, we compare these methods with Local Search methods as well. We also empirically compare Answer Set Programming with Propositional Satisfiability, for SMTI instances. This paper is under consideration for acceptance in Theory and Practice of Logic Programming (TPLP).