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Matching couples with Scarf’s algorithm

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Abstract

Scarf’s algorithm (Scarf, H. E. Econometrica 35, 50–69 1967) provides fractional core elements for NTU-games. Biró and Fleiner [4] showed that Scarf’s algorithm can be extended for capacitated NTU-games. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with different intensities up to some limits, and the contribution of the agents can also differ in a coalition. The fractional stable solutions for the above model, produced by the extended Scarf algorithm, are called stable allocations. In this paper we apply this solution concept for the Hospitals / Residents problem with Couples (HRC). This is one of the most important general stable matching problems due to its relevant applications, also well-known to be NP-hard. We show that if a stable allocation yielded by the Scarf algorithm turns out to be integral then it provides a stable matching for an instance of HRC, so this method can be used as a heuristic. In an experimental study, we compare this method with other heuristics constructed for HRC that have been applied in practice in the American and Scottish resident allocation programs, respectively. Our main finding is that the Scarf algorithm outperforms all the other known heuristics when the proportion of couples is high.

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Authors and Affiliations

  1. Institute of Economics, Research Centre for Economic and Regional Studies, Hungarian Academy of Sciences, H-1112, Budaörsi út 45, Budapest, Hungary

    Péter Biró

  2. Department of Operations Research and Actuarial Sciences, Corvinus University of Budapest, Fővám tér 13-15, 1093, Budapest, Hungary

    Péter Biró

  3. Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Magyar tudósok körútja 2, 1117, Budapest, Hungary

    Tamás Fleiner

  4. School of Computing Science, University of Glasgow, Sir Alwyn Williams Building, G12 8QQ, Glasgow, UK

    Robert W. Irving

Authors
  1. Péter Biró
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  2. Tamás Fleiner
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  3. Robert W. Irving
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Corresponding author

Correspondence to Péter Biró.

Additional information

Péter Biró, Supported by the Hungarian Academy of Sciences under its Momentum Programme (LD-004/2010), by the Hungarian Scientific Research Fund - OTKA (no. K108673), and by János Bolyai Research Scholarship of the Hungarian Academy of Sciences. Tamás Fleiner a member of the MTA-ELTE Egerváry Research Group. The research was supported by the Hungarian Scientific Research Fund - OTKA (no. K108383).

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Biró, P., Fleiner, T. & Irving, R.W. Matching couples with Scarf’s algorithm. Ann Math Artif Intell 77, 303–316 (2016). https://doi.org/10.1007/s10472-015-9491-5

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  • DOI: https://doi.org/10.1007/s10472-015-9491-5

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