TY - GEN
T1 - Many-to-many stable matchings with ties, master preference lists, and matroid constraints
AU - Kamiyama, Naoyuki
N1 - Funding Information:
This research was supported by JST PRESTO Grant Number JPMJPR1753. Japan.
Publisher Copyright:
© 2019 International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
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M3 - Conference contribution
AN - SCOPUS:85076848256
T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
SP - 583
EP - 591
BT - 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019
PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
T2 - 18th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2019
Y2 - 13 May 2019 through 17 May 2019
ER -