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

Irving, R.W. and Manlove, D.F. (2008) Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems. Journal of Combinatorial Optimization, 16(3), pp. 279-292. (doi: 10.1007/s10878-007-9133-x)



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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.

Item Type:Articles
Additional Information:The original publication is available at
Keywords:Stable matching, weak stability, NP-hard problems, approximation algorithms
Glasgow Author(s) Enlighten ID:Manlove, Professor David and Irving, Dr Robert
Authors: Irving, R.W., 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:23 December 2007
Copyright Holders:Copyright © 2008 Springer Verlag
First Published:First published in Journal of Combinatorial Optimization 16(3):279-292
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher including additional information statement.

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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/E011993/1Computing Science