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.2018.17
URN: urn:nbn:de:0030-drops-99164
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9916/
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Cseh, Ágnes ; Kavitha, Telikepalli

Popular Matchings in Complete Graphs

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LIPIcs-FSTTCS-2018-17.pdf (0.4 MB)

Abstract

Our input is a complete graph G = (V,E) on n vertices where each vertex has a strict ranking of all other vertices in G. The goal is to construct a matching in G that is "globally stable" or popular. A matching M is popular if M does not lose a head-to-head election against any matching M': here each vertex casts a vote for the matching in {M,M'} where it gets a better assignment. Popular matchings need not exist in the given instance G and the popular matching problem is to decide whether one exists or not. The popular matching problem in G is easy to solve for odd n. Surprisingly, the problem becomes NP-hard for even n, as we show here.

BibTeX - Entry

@InProceedings{cseh_et_al:LIPIcs:2018:9916,
  author =	{Ágnes Cseh and Telikepalli Kavitha},
  title =	{{Popular Matchings in Complete Graphs}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software  Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{17:1--17:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Sumit Ganguly and Paritosh Pandya},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9916},
  URN =		{urn:nbn:de:0030-drops-99164},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.17},
  annote =	{Keywords: popular matching, complete graph, complexity, linear programming}
}

Keywords: popular matching, complete graph, complexity, linear programming
Collection: 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)
Issue Date: 2018
Date of publication: 05.12.2018

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