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.2017.19
URN: urn:nbn:de:0030-drops-83765
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8376/
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Brandl, Florian ; Kavitha, Telikepalli

Popular Matchings with Multiple Partners

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LIPIcs-FSTTCS-2017-19.pdf (0.5 MB)

Abstract

Our input is a bipartite graph G=(A\cup B,E) where each vertex in A\cup B has a preference list strictly ranking its neighbors. The vertices in A and in B are called students and courses, respectively. Each student a seeks to be matched to cap(a)\geq 1 many courses while each course b seeks cap(b)\geq 1 many students to be matched to it. The Gale-Shapley algorithm computes a pairwise-stable matching (one with no blocking edge) in G in linear time. We consider the problem of computing a popular matching in G - a matching M is popular if M cannot lose an election to any matching where vertices cast votes for one matching versus another. Our main contribution is to show that a max-size popular matching in G can be computed by the 2-level Gale-Shapley algorithm in linear time. This is an extension of the classical Gale-Shapley algorithm and we prove its correctness via linear programming.

BibTeX - Entry

@InProceedings{brandl_et_al:LIPIcs:2018:8376,
  author =	{Florian Brandl and Telikepalli Kavitha},
  title =	{{Popular Matchings with Multiple Partners}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{19:1--19:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8376},
  URN =		{urn:nbn:de:0030-drops-83765},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.19},
  annote =	{Keywords: Bipartite graphs, Linear programming duality, Gale-Shapley algorithm}
}

Keywords: Bipartite graphs, Linear programming duality, Gale-Shapley algorithm
Collection: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 12.02.2018

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