On the (parameterized) complexity of almost stable marriage

Sushmita Gupta, Pallavi Jain, Sanjukta Roy, Saket Saurabh, Meirav Zehavi

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

6 Scopus citations

Abstract

In the Stable Marriage problem, when the preference lists are complete, all agents of the smaller side can be matched. However, this need not be true when preference lists are incomplete. In most real-life situations, where agents participate in the matching market voluntarily and submit their preferences, it is natural to assume that each agent wants to be matched to someone in his/her preference list as opposed to being unmatched. In light of the Rural Hospital Theorem, we have to relax the “no blocking pair” condition for stable matchings in order to match more agents. In this paper, we study the question of matching more agents with fewest possible blocking edges. In particular, the goal is to find a matching whose size exceeds that of a stable matching in the graph by at least t and has at most k blocking edges. We study this question in the realm of parameterized complexity with respect to several natural parameters, k, t, d, where d is the maximum length of a preference list. Unfortunately, the problem remains intractable even for the combined parameter k + t + d. Thus, we extend our study to the local search variant of this problem, in which we search for a matching that not only fulfills each of the above conditions but is “closest”, in terms of its symmetric difference to the given stable matching, and obtain an FPT algorithm.

Original languageEnglish
Title of host publication40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2020
EditorsNitin Saxena, Sunil Simon
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771740
DOIs
StatePublished - 1 Dec 2020
Event40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2020 - Virtual, Goa, India
Duration: 14 Dec 202018 Dec 2020

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume182
ISSN (Print)1868-8969

Conference

Conference40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2020
Country/TerritoryIndia
CityVirtual, Goa
Period14/12/2018/12/20

Keywords

  • Local Search
  • Parameterized Complexity
  • Stable Matching

ASJC Scopus subject areas

  • Software

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