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DOI: 10.4230/LIPIcs.CP.2022.16

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

Authors: Ágnes Cseh, Guillaume Escamocher, and Luis Quesada

Published in: LIPIcs, Volume 235, 28th International Conference on Principles and Practice of Constraint Programming (CP 2022)

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.

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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)

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@InProceedings{cseh_et_al:LIPIcs.CP.2022.16,
  author =	{Cseh, \'{A}gnes and Escamocher, Guillaume and Quesada, Luis},
  title =	{{Computing Relaxations for the Three-Dimensional Stable Matching Problem with Cyclic Preferences}},
  booktitle =	{28th International Conference on Principles and Practice of Constraint Programming (CP 2022)},
  pages =	{16:1--16:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-240-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{235},
  editor =	{Solnon, Christine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2022.16},
  URN =		{urn:nbn:de:0030-drops-166450},
  doi =		{10.4230/LIPIcs.CP.2022.16},
  annote =	{Keywords: Three-dimensional stable matching with cyclic preferences, 3dsm-cyc, Constraint Programming, relaxation, almost stable matching}
}

Document

DOI: 10.4230/LIPIcs.CP.2021.22

A Collection of Constraint Programming Models for the Three-Dimensional Stable Matching Problem with Cyclic Preferences

Authors: Ágnes Cseh, Guillaume Escamocher, Begüm Genç, and Luis Quesada

Published in: LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)

Abstract

We introduce five constraint models for the 3-dimensional stable matching problem with cyclic preferences and study their relative performances under diverse configurations. While several constraint models have been proposed for variants of the two-dimensional stable matching problem, we are the first to present constraint models for a higher number of dimensions. We show for all five models how to capture two different stability notions, namely weak and strong stability. Additionally, we translate some well-known fairness notions (i.e. sex-equal, minimum regret, egalitarian) into 3-dimensional matchings, and present how to capture them in each model. Our tests cover dozens of problem sizes and four different instance generation methods. We explore two levels of commitment in our models: one where we have an individual variable for each agent (individual commitment), and another one where the determination of a variable involves pairing the three agents at once (group commitment). Our experiments show that the suitability of the commitment depends on the type of stability we are dealing with. Our experiments not only led us to discover dependencies between the type of stability and the instance generation method, but also brought light to the role that learning and restarts can play in solving this kind of problems.

Cite as

Ágnes Cseh, Guillaume Escamocher, Begüm Genç, and Luis Quesada. A Collection of Constraint Programming Models for the Three-Dimensional Stable Matching Problem with Cyclic Preferences. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cseh_et_al:LIPIcs.CP.2021.22,
  author =	{Cseh, \'{A}gnes and Escamocher, Guillaume and Gen\c{c}, Beg\"{u}m and Quesada, Luis},
  title =	{{A Collection of Constraint Programming Models for the Three-Dimensional Stable Matching Problem with Cyclic Preferences}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-211-2},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{210},
  editor =	{Michel, Laurent D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.22},
  URN =		{urn:nbn:de:0030-drops-153137},
  doi =		{10.4230/LIPIcs.CP.2021.22},
  annote =	{Keywords: Three-dimensional stable matching with cyclic preferences, 3DSM-cyc, Constraint Programming, fairness}
}

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

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A Collection of Constraint Programming Models for the Three-Dimensional Stable Matching Problem with Cyclic Preferences

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