The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences

McKay, M. and Manlove, D. (2021) The Three-Dimensional Stable Roommates Problem with Additively Separable Preferences. In: 14th International Symposium on Algorithmic Game Theory (SAGT 2021), Aarhus, Denmark, 21-24 Sep 2021, pp. 266-280. ISBN 9783030859466 (doi:10.1007/978-3-030-85947-3_18)

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Abstract

The Stable Roommates problem involves matching a set of agents into pairs based on the agents’ strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A number of three-dimensional variants exist, in which agents are instead matched into triples. Both the original problem and these variants can also be viewed as hedonic games. We formalise a three-dimensional variant using general additively separable preferences, in which each agent provides an integer valuation of every other agent. In this variant, we show that a stable matching may not exist and that the related decision problem is NP -complete, even when the valuations are binary. In contrast, we show that if the valuations are binary and symmetric then a stable matching must exist and can be found in polynomial time. We also consider the related problem of finding a stable matching with maximum utilitarian welfare when valuations are binary and symmetric. We show that this optimisation problem is NP -hard and present a novel 2-approximation algorithm.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Manlove, Professor David and McKay, Mr Michael
Authors: McKay, M., and Manlove, D.
College/School:College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783030859466
Copyright Holders:Copyright © 2021 Springer Nature Switzerland AG
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
305200DTP 2018-19 University of GlasgowMary Beth KneafseyEngineering and Physical Sciences Research Council (EPSRC)EP/R513222/1MVLS - Graduate School
300808IP-MATCH: Integer Programming for Large and Complex Matching ProblemsDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)EP/P028306/1Computing Science