The Stable Roommates Problem with Short Lists

Cseh, A., Manlove, D. and Irving, R. W. (2016) The Stable Roommates Problem with Short Lists. In: 9th International Symposium on Algorithmic Game Theory (SAGT), Liverpool, UK, 19-21 Sept 2016, pp. 207-219. ISBN 9783662533536 (doi:10.1007/978-3-662-53354-3_17)

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Abstract

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, egal d-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 NPNP -hard even if d=3d=3 . On the positive side we give a 2d+372d+37 -approximation algorithm for d∈{3,4,5}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 NPNP -complete even if d=3d=3 . We also consider the “most stable” version of this problem and prove a strong inapproximability bound for the d=3d=3 case. However for d=2d=2 we show that the latter problem can be solved in polynomial time.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Dr David and Irving, Dr Robert
Authors: Cseh, A., Manlove, D., and Irving, R. W.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Lecture Notes in Computer Science
Publisher:Springer
ISSN:0302-9743
ISBN:9783662533536
Published Online:01 September 2016
Copyright Holders:Copyright © 2016 Springer-Verlag
First Published:First published in Lecture Notes in Computer Science 9928: 207-219
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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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