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

Jiehua Chen, Danny Hermelin, Manuel Sorge, Harel Yedidsion

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

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.

Original languageAmerican English
Title of host publication45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
EditorsChristos Kaklamanis, Daniel Marx, Ioannis Chatzigiannakis, Donald Sannella
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770767
DOIs
StatePublished - 1 Jul 2018
Event45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 - Prague, Czech Republic
Duration: 9 Jul 201813 Jul 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume107

Conference

Conference45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
Country/TerritoryCzech Republic
CityPrague
Period9/07/1813/07/18

Keywords

  • Analysis and algorithmics
  • Data reduction rules
  • Kernelizations
  • NP-hard problems
  • Parameterized complexity

All Science Journal Classification (ASJC) codes

  • Software

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