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Matching couples with Scarf’s algorithm

Matching couples with Scarf’s algorithm 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Matching couples with Scarf’s algorithm

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References (6)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer International Publishing Switzerland
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-015-9491-5
Publisher site
See Article on Publisher Site

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.

Journal

Annals of Mathematics and Artificial Intelligence – Springer Journals

Published: Nov 25, 2015

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