2014 Fiscal Year Final Research Report
A Study on Discrete Structures of Advanced Stable Matching Problems
| Project/Area Number |
25730006
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Theory of informatics
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| Research Institution | Kyushu University |
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Principal Investigator |
KAMIYAMA Naoyuki 九州大学, マス・フォア・インダストリ研究所, 准教授 (10548134)
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| Project Period (FY) |
2013-04-01 – 2015-03-31
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| Keywords | 安定マッチング / マトロイド |
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| Outline of Final Research Achievements |
In this research, we considered advanced stable matching problems, such as the Pareto stable matching problem, a matching problem with lower quotas, the popular matching problem.
Our contribution can be summarized as follows. (1) For the Pareto stable matching problem, we proposed a new approach that is different from the algorithm of Chen. Our algorithm can be regarded as an extension of the algorithm Gale and Shapley for the stable matching problem. (2) For a matching problem with lower quotas, we proved that the mechanism proposed by Monte and Tumennasan can be extended to a more general setting. (3) For the popular matching problem, we introduced a matroid generalization of the popular matching problem, and proved that if there exists no tie in preference lists, then we can solve this problem in polynomial time by extending the algorithm of Abraham et al. for the popular matching problem.
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| Free Research Field |
離散最適化
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