Socially stable matchings in the hospitals / residents problem

Askalidis, G., Immorlica, N., Kwanashie, A., Manlove, D.F. and Pountourakis, E. (2013) Socially stable matchings in the hospitals / residents problem. Lecture Notes in Computer Science, 8037, pp. 85-96. (doi:10.1007/978-3-642-40104-6_8)

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Abstract

In the Hospitals/Residents (HR) problem, agents are partitioned into hospitals and residents. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. Such a situation is undesirable as it could lead to a deviation in which the blocking pair form a private arrangement outside the matching. This however assumes that the blocking pair have social ties or communication channels to facilitate the deviation. Relaxing the stability definition to take account of the potential lack of social ties between agents can yield larger stable matchings. In this paper, we define the Hospitals/Residents problem under Social Stability (HRSS) which takes into account social ties between agents by introducing a social network graph to the HR problem. Edges in the social network graph correspond to resident-hospital pairs in the HR instance that know one another. Pairs that do not have corresponding edges in the social network graph can belong to a matching M but they can never block M. Relative to a relaxed stability definition for HRSS, called social stability, we show that socially stable matchings can have different sizes and the problem of finding a maximum socially stable matching is NP-hard, though approximable within 3/2. Furthermore we give polynomial time algorithms for three special cases of the problem.

Item Type:Articles
Additional Information:The final publication is available at link.springer.com
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David
Authors: Askalidis, G., Immorlica, N., Kwanashie, A., Manlove, D.F., and Pountourakis, E.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Lecture Notes in Computer Science
Publisher:Springer Verlag
ISSN:0302-9743
ISSN (Online):1611-3349
Copyright Holders:Copyright © 2013 Springer Verlag
First Published:First published in Lecture Notes in Computer Science 8037:85-96
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
607071Efficient Algorithms for Mechanism Design Without Monetary Transfer.David ManloveEngineering & Physical Sciences Research Council (EPSRC)EP/K010042/1COM - COMPUTING SCIENCE