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A General Framework for Stable Roommates Problems using Answer Set Programming

Published online by Cambridge University Press:  22 September 2020

ESRA ERDEM Open the ORCID record for ESRA ERDEM [Opens in a new window] ,
MÜGE FIDAN ,
DAVID MANLOVE  and
PATRICK PROSSER
ESRA ERDEM
Affiliation:
Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkeyesraerdem@sabanciuniv.edu, mugefidan@sabanciuniv.edu
MÜGE FIDAN
Affiliation:
Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkeyesraerdem@sabanciuniv.edu, mugefidan@sabanciuniv.edu
DAVID MANLOVE
Affiliation:
School of Computing Science, University of Glasgow, Glasgow, UKdavid.manlove@glasgow.ac.uk, patrick.prosser@glasgow.ac.uk
PATRICK PROSSER
Affiliation:
School of Computing Science, University of Glasgow, Glasgow, UKdavid.manlove@glasgow.ac.uk, patrick.prosser@glasgow.ac.uk
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Abstract

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The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that each pair shares a room, and there is no pair of agents that would block this matching (i.e., who prefers the other to their roommate in the matching). There are interesting variations of SR that are motivated by applications (e.g., the preference lists may be incomplete (SRI) and involve ties (SRTI)), and that try to find a more fair solution (e.g., Egalitarian SR). Unlike the Stable Marriage problem, every SR instance is not guaranteed to have a solution. For that reason, there are also variations of SR that try to find a good-enough solution (e.g., Almost SR). Most of these variations are NP-hard. We introduce a formal framework, called SRTI-ASP, utilizing the logic programming paradigm Answer Set Programming, that is provable and general enough to solve many of such variations of SR. Our empirical analysis shows that SRTI-ASP is also promising for applications.

Keywords

stable roommates problemanswer set programmingdeclarative problem solving
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 20 , Issue 6: 36th International Conference on Logic Programming Special Issue II , November 2020 , pp. 911 - 925
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Footnotes

*

This work has been partially supported by Sabanci University IRP Grant, and the Scottish Informatics and Computer Science Alliance DVF Programme. The third and fourth authors were supported by grants EP/P028306/1 and EP/P026842/1 from the Engineering and Physical Sciences Research Council, respectively.

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