The Stable Roommates problem with short lists

Cseh, A., Irving, R. W. and Manlove, D. F. (2019) The Stable Roommates problem with short lists. Theory of Computing Systems, 63(1), pp. 128-149. (doi: 10.1007/s00224-017-9810-9)

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We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists (sri) that are degree constrained, i.e., preference lists are of bounded length. The first variant, egald-sri, involves finding an egalitarian stable matching in solvable instances of sri with preference lists of length at most d. We show that this problem is NP-hard even if d = 3. On the positive side we give a 2d+372d+37-approximation algorithm for d ∈{3,4,5} which improves on the known bound of 2 for the unbounded preference list case. In the second variant of sri, called d-srti, preference lists can include ties and are of length at most d. We show that the problem of deciding whether an instance of d-srti admits a stable matching is NP-complete even if d = 3. We also consider the “most stable” version of this problem and prove a strong inapproximability bound for the d = 3 case. However for d = 2 we show that the latter problem can be solved in polynomial time.

Item Type:Articles
Additional Information:The authors were supported by the Hungarian Academy of Sciences under its Momentum Programme (LP2016-3/2016), its János Bolyai Research Fellowship, OTKA grant K108383, COST Action IC1205 on Computational Social Choice and by EPSRC grant EP/K010042/1.
Glasgow Author(s) Enlighten ID:Irving, Dr Robert and Manlove, Professor David
Authors: Cseh, A., Irving, R. W., and Manlove, D. F.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Theory of Computing Systems
Publisher:Springer Verlag
ISSN (Online):1433-0490
Published Online:01 October 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Theory of Computing Systems 63:128–149
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
607071Efficient Algorithms for Mechanism Design Without Monetary Transfer.David ManloveEngineering and Physical Sciences Research Council (EPSRC)EP/K010042/1COM - COMPUTING SCIENCE