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.2019.20
URN: urn:nbn:de:0030-drops-115820
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11582/
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Kavitha, Telikepalli

Popular Roommates in Simply Exponential Time

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LIPIcs-FSTTCS-2019-20.pdf (0.5 MB)

Abstract

We consider the popular matching problem in a graph G = (V,E) on n vertices with strict preferences. A matching M is popular if there is no matching N in G such that vertices that prefer N to M outnumber those that prefer M to N. It is known that it is NP-hard to decide if G has a popular matching or not. There is no faster algorithm known for this problem than the brute force algorithm that could take n! time. Here we show a simply exponential time algorithm for this problem, i.e., one that runs in O^*(k^n) time, where k is a constant.
We use the recent breakthrough result on the maximum number of stable matchings possible in such instances to analyze our algorithm for the popular matching problem. We identify a natural (also, hard) subclass of popular matchings called truly popular matchings and show an O^*(2^n) time algorithm for the truly popular matching problem.

BibTeX - Entry

@InProceedings{kavitha:LIPIcs:2019:11582,
  author =	{Telikepalli Kavitha},
  title =	{{Popular Roommates in Simply Exponential Time}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{20:1--20:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Arkadev Chattopadhyay and Paul Gastin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11582},
  URN =		{urn:nbn:de:0030-drops-115820},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.20},
  annote =	{Keywords: Roommates instance, Popular matching, Stable matching, Dual certificate}
}

Keywords: Roommates instance, Popular matching, Stable matching, Dual certificate
Collection: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Issue Date: 2019
Date of publication: 04.12.2019

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