TY - JOUR

T1 - How hard is it to satisfy (Almost) all roommates?

AU - Chen, Jiehua

AU - Hermelin, Dan

AU - Sorge, Manuel

AU - Yedidsion, Harel

N1 - Publisher Copyright:
© Jiehua Chen, Danny Hermelin, Manuel Sorge, and Harel Yedidsion;.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - The classic Stable Roommates problem (the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint pairs such that no two agents induce a blocking pair. Herein, each agent has a preference list denoting who it prefers to have as a partner, and two agents are blocking if they prefer to be with each other rather than with their assigned partners. Since stable matchings may not be unique, we study an NP-hard optimization variant of Stable Roommates, called Egal Stable Roommates, which seeks to find a stable matching with a minimum egalitarian cost γ, i.e. the sum of the dissatisfaction of the agents is minimum. The dissatisfaction of an agent is the number of agents that this agent prefers over its partner if it is matched; otherwise it is the length of its preference list. We also study almost stable matchings, called Min-Block-Pair Stable Roommates, which seeks to find a matching with a minimum number β of blocking pairs. Our main result is that Egal Stable Roommates parameterized by γ is fixed-parameter tractable, while Min-Block-Pair Stable Roommates parameterized by β is W[1]-hard, even if the length of each preference list is at most five.

AB - The classic Stable Roommates problem (the non-bipartite generalization of the well-known Stable Marriage problem) asks whether there is a stable matching for a given set of agents, i.e. a partitioning of the agents into disjoint pairs such that no two agents induce a blocking pair. Herein, each agent has a preference list denoting who it prefers to have as a partner, and two agents are blocking if they prefer to be with each other rather than with their assigned partners. Since stable matchings may not be unique, we study an NP-hard optimization variant of Stable Roommates, called Egal Stable Roommates, which seeks to find a stable matching with a minimum egalitarian cost γ, i.e. the sum of the dissatisfaction of the agents is minimum. The dissatisfaction of an agent is the number of agents that this agent prefers over its partner if it is matched; otherwise it is the length of its preference list. We also study almost stable matchings, called Min-Block-Pair Stable Roommates, which seeks to find a matching with a minimum number β of blocking pairs. Our main result is that Egal Stable Roommates parameterized by γ is fixed-parameter tractable, while Min-Block-Pair Stable Roommates parameterized by β is W[1]-hard, even if the length of each preference list is at most five.

KW - Analysis and algorithmics

KW - Data reduction rules

KW - Kernelizations

KW - NP-hard problems

KW - Parameterized complexity

UR - http://www.scopus.com/inward/record.url?scp=85049780267&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2018.35

DO - 10.4230/LIPIcs.ICALP.2018.35

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AN - SCOPUS:85049780267

JO - Leibniz International Proceedings in Informatics, LIPIcs

JF - Leibniz International Proceedings in Informatics, LIPIcs

SN - 1868-8969

Y2 - 9 July 2018 through 13 July 2018

ER -