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Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems

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  • Robert W. Irving

    (University of Glasgow)

  • David F. Manlove

    (University of Glasgow)

Abstract

When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes.

Suggested Citation

  • Robert W. Irving & David F. Manlove, 2008. "Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems," Journal of Combinatorial Optimization, Springer, vol. 16(3), pages 279-292, October.
    • Handle: RePEc:spr:jcomop:v:16:y:2008:i:3:d:10.1007_s10878-007-9133-x
    DOI: 10.1007/s10878-007-9133-x
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    References listed on IDEAS

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    1. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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    Cited by:

    1. Ágoston, Kolos Csaba & Biró, Péter & Kováts, Endre & Jankó, Zsuzsanna, 2022. "College admissions with ties and common quotas: Integer programming approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 722-734.
    2. Christian Haas, 2021. "Two-Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1115-1148, April.
    3. Kolos Csaba Ágoston & Péter Biró & Iain McBride, 2016. "Integer programming methods for special college admissions problems," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1371-1399, November.
    4. Enrico Maria Fenoaltea & Izat B. Baybusinov & Jianyang Zhao & Lei Zhou & Yi-Cheng Zhang, 2021. "The Stable Marriage Problem: an Interdisciplinary Review from the Physicist's Perspective," Papers 2103.11458, arXiv.org.
    5. Ágoston, Kolos Csaba & Biró, Péter & Szántó, Richárd, 2018. "Stable project allocation under distributional constraints," Operations Research Perspectives, Elsevier, vol. 5(C), pages 59-68.

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