Many-to-many stable matchings with ties, master preference lists, and matroid constraints

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Abstract

In this paper, we consider a matroid generalization of the hospitals/residents problem with ties. Especially, we focus on the situation in which we are given a master list and the preference list of each hospital over residents is derived from this master list. In this setting, Kamiyama proved that if hospitals have matroid constraints and each resident is assigned to at most one hospital, then we can solve the super-stable matching problem and the strongly stable matching problem in polynomial time. In this paper, we generalize these results to the many-to-many setting. More specifically, we consider the setting where each resident can be assigned to multiple hospitals, and the set of hospitals that this resident is assigned to must form an independent set of a matroid. In this paper, we prove that the super-stable matching problem and the strongly stable matching problem in this setting can be solved in polynomial time.

Original languageEnglish
Title of host publication18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages583-591
Number of pages9
ISBN (Electronic)9781510892002
Publication statusPublished - Jan 1 2019
Event18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019 - Montreal, Canada
Duration: May 13 2019May 17 2019

Publication series

NameProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
Volume1
ISSN (Print)1548-8403
ISSN (Electronic)1558-2914

Conference

Conference18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019
CountryCanada
CityMontreal
Period5/13/195/17/19

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All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering

Cite this

Kamiyama, N. (2019). Many-to-many stable matchings with ties, master preference lists, and matroid constraints. In 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019 (pp. 583-591). (Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS; Vol. 1). International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS).