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DOI: 10.4230/LIPIcs.ISAAC.2017.56
URN: urn:nbn:de:0030-drops-82244
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8224/
Miyazaki, Shuichi ; Okamoto, Kazuya
Jointly Stable Matchings
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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 L_i (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 L_i. We show that the decision problem is NP-complete already for k=2, even if each person's preference list is of length at most four, while 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 L_i, then the problem can be solved in linear time.
BibTeX - Entry
@InProceedings{miyazaki_et_al:LIPIcs:2017:8224,
author = {Shuichi Miyazaki and Kazuya Okamoto},
title = {{Jointly Stable Matchings}},
booktitle = {28th International Symposium on Algorithms and Computation (ISAAC 2017)},
pages = {56:1--56:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-054-5},
ISSN = {1868-8969},
year = {2017},
volume = {92},
editor = {Yoshio Okamoto and Takeshi Tokuyama},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2017/8224},
URN = {urn:nbn:de:0030-drops-82244},
doi = {10.4230/LIPIcs.ISAAC.2017.56},
annote = {Keywords: stable marriage problem, stable matching, NP-completeness, linear time algorithm}
}
| Keywords: | stable marriage problem, stable matching, NP-completeness, linear time algorithm | |
| Seminar: | 28th International Symposium on Algorithms and Computation (ISAAC 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 07.12.2017 |
