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Computing Relaxations for the Three-Dimensional Stable Matching Problem with Cyclic Preferences

Authors Ágnes Cseh , Guillaume Escamocher , Luis Quesada

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Author Details

Ágnes Cseh
  • Institute of Economics, Centre for Economic and Regional Studies, Budapest, Hungary
Guillaume Escamocher
  • Insight Centre for Data Analytics, School of Computer Science and Information Technology, University College Cork, Ireland
Luis Quesada
  • Insight Centre for Data Analytics, School of Computer Science and Information Technology, University College Cork, Ireland

Funding

This publication has emanated from research conducted with the financial support of Science Foundation Ireland under Grant numbers 12/RC/2289-P2 and 16/SP/3804, which are co-funded under the European Regional Development Fund. Cseh was supported by OTKA grant K128611 and the János Bolyai Research Fellowship.

Acknowledgements

COST Action CA16228 European Network for Game Theory.

Cite As Get BibTex

Ágnes Cseh, Guillaume Escamocher, and Luis Quesada. Computing Relaxations for the Three-Dimensional Stable Matching Problem with Cyclic Preferences. In 28th International Conference on Principles and Practice of Constraint Programming (CP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 235, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.CP.2022.16

Abstract

Constraint programming has proven to be a successful framework for determining whether a given instance of the three-dimensional stable matching problem with cyclic preferences (3dsm-cyc) admits a solution. If such an instance is satisfiable, constraint models can even compute its optimal solution for several different objective functions. On the other hand, the only existing output for unsatisfiable 3dsm-cyc instances is a simple declaration of impossibility.
In this paper, we explore four ways to adapt constraint models designed for 3dsm-cyc to the maximum relaxation version of the problem, that is, the computation of the smallest part of an instance whose modification leads to satisfiability. We also extend our models to support the presence of costs on elements in the instance, and to return the relaxation with lowest total cost for each of the four types of relaxation. Empirical results reveal that our relaxation models are efficient, as in most cases, they show little overhead compared to the satisfaction version.

Subject Classification

ACM Subject Classification
  • Theory of computation → Constraint and logic programming
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Three-dimensional stable matching with cyclic preferences
  • 3dsm-cyc
  • Constraint Programming
  • relaxation
  • almost stable matching

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