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Title: Jointly stable matchings
Authors: Miyazaki, Shuichi  kyouindb  KAKEN_id  orcid https://orcid.org/0000-0003-0369-1970 (unconfirmed)
Okamoto, Kazuya  kyouindb  KAKEN_id  orcid https://orcid.org/0000-0002-9079-2253 (unconfirmed)
Author's alias: 宮崎, 修一
岡本, 和也
Keywords: Stable marriage problem
Stable matching
NP-completeness
Linear time algorithm
Issue Date: Aug-2019
Publisher: Springer US
Journal title: Journal of Combinatorial Optimization
Volume: 38
Issue: 2
Start page: 646
End page: 665
Abstract: In the stable marriage problem, we are given a set of men, a set of women, and each person’s preference list. Our task is to find a stable matching, that is, a matching admitting no unmatched (man, woman)-pair each of which improves the situation by being matched together. It is known that any instance admits at least one stable matching. In this paper, we consider a natural extension where k( ≥ 2) sets of preference lists Li (1≤ i ≤ k ) over the same set of people are given, and the aim is to find a jointly stable matching, a matching that is stable with respect to all Li . We show that the decision problem is NP-complete for the following two restricted cases; (1) k = 2 and each person’s preference list is of length at most four, and (2) k = 4 , each man’s preference list is of length at most three, and each woman’s preference list is of length at most four. On the other hand, we show that it is solvable in linear time for any k if each man’s preference list is of length at most two (women’s lists can be of unbounded length). We also show that if each woman’s preference lists are same in all Li , then the problem can be solved in linear time.
Rights: This is a post-peer-review, pre-copyedit version of an article published in 'Journal of Combinatorial Optimization'. The final authenticated version is available online at: https://doi.org/10.1007/s10878-019-00402-4.
The full-text file will be made open to the public on 19 March 2020 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
URI: http://hdl.handle.net/2433/243846
DOI(Published Version): 10.1007/s10878-019-00402-4
Appears in Collections:Journal Articles

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