Keeping partners together: algorithmic results for the hospitals/residents problem with couples

McDermid, E.J. and Manlove, D.F. (2010) Keeping partners together: algorithmic results for the hospitals/residents problem with couples. Journal of Combinatorial Optimization, 19(3), pp. 279-303. (doi: 10.1007/s10878-009-9257-2)

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The Hospitals/Residents problem with Couples (HRC) is a generalisation of the classical Hospitals/Residents problem (HR) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of hospitals (h i ,h j ). We consider a natural restriction of HRC in which the members of a couple have individual preference lists over hospitals, and the joint preference list of the couple is consistent with these individual lists in a precise sense. We give an appropriate stability definition and show that, in this context, the problem of deciding whether a stable matching exists is NP-complete, even if each resident’s preference list has length at most 3 and each hospital has capacity at most 2. However, with respect to classical (Gale-Shapley) stability, we give a linear-time algorithm to find a stable matching or report that none exists, regardless of the preference list lengths or the hospital capacities. Finally, for an alternative formulation of our restriction of HRC, which we call the Hospitals/Residents problem with Sizes (HRS), we give a linear-time algorithm that always finds a stable matching for the case that hospital preference lists are of length at most 2, and where hospital capacities can be arbitrary.

Item Type:Articles
Additional Information:The original publication is available at
Glasgow Author(s) Enlighten ID:Manlove, Professor David and McDermid, Mr Eric
Authors: McDermid, E.J., and Manlove, D.F.
Subjects:Q Science > QA Mathematics > QA75 Electronic computers. Computer science
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Journal of Combinatorial Optimization
ISSN (Online):1573-2886
Published Online:27 August 2009
Copyright Holders:Copyright © 2010 Springer
First Published:First published in Journal of Combinatorial Optimization 19(3):279-303
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
320021Algorithmics of Stable Matching Problems with IndifferenceDavid ManloveEngineering & Physical Sciences Research Council (EPSRC)GR/R84597/01Computing Science
436361MATCH-UP - matching under preferences - algorithms and complexityRobert IrvingEngineering & Physical Sciences Research Council (EPSRC)EP/E011993/1COM - COMPUTING SCIENCE