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Strongly Stable Matchings under Matroid Constraints

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  • Naoyuki Kamiyama

Abstract

We consider a many-to-one variant of the stable matching problem. More concretely, we consider the variant of the stable matching problem where one side has a matroid constraint. Furthermore, we consider the situation where the preference of each agent may contain ties. In this setting, we consider the problem of checking the existence of a strongly stable matching, and finding a strongly stable matching if a strongly stable matching exists. We propose a polynomial-time algorithm for this problem.

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  • Naoyuki Kamiyama, 2022. "Strongly Stable Matchings under Matroid Constraints," Papers 2208.11272, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2208.11272
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    References listed on IDEAS

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    1. Sofiat Olaosebikan & David Manlove, 2022. "Super-stability in the student-project allocation problem with ties," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1203-1239, July.
    2. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
    3. Tamás Fleiner & Naoyuki Kamiyama, 2016. "A Matroid Approach to Stable Matchings with Lower Quotas," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 734-744, May.
    4. Yu Yokoi, 2017. "A Generalized Polymatroid Approach to Stable Matchings with Lower Quotas," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 238-255, January.
    5. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    6. Satoru Fujishige & Akihisa Tamura, 2007. "A Two-Sided Discrete-Concave Market with Possibly Bounded Side Payments: An Approach by Discrete Convex Analysis," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 136-155, February.
    7. Kazuo Murota & Yu Yokoi, 2015. "On the Lattice Structure of Stable Allocations in a Two-Sided Discrete-Concave Market," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 460-473, February.
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