License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2020.24
URN: urn:nbn:de:0030-drops-132655
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Gupta, Sushmita ; Jain, Pallavi ; Roy, Sanjukta ; Saurabh, Saket ; Zehavi, Meirav

On the (Parameterized) Complexity of Almost Stable Marriage

LIPIcs-FSTTCS-2020-24.pdf (0.9 MB)


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.

BibTeX - Entry

  author =	{Sushmita Gupta and Pallavi Jain and Sanjukta Roy and Saket Saurabh and Meirav Zehavi},
  title =	{{On the (Parameterized) Complexity of Almost Stable Marriage}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{24:1--24:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Nitin Saxena and Sunil Simon},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-132655},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.24},
  annote =	{Keywords: Stable Matching, Parameterized Complexity, Local Search}

Keywords: Stable Matching, Parameterized Complexity, Local Search
Collection: 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)
Issue Date: 2020
Date of publication: 04.12.2020

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