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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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, 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 |
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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. |
Status: | Published |
Refereed: | Yes |
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: | 1432-4350 |
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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