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.2013.339
URN: urn:nbn:de:0030-drops-43841
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4384/
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Huang, Chien-Chung ; Kavitha, Telikepalli ; Mehlhorn, Kurt ; Michail, Dimitrios

Fair Matchings and Related Problems

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Abstract

Let G = (A union B, E) be a bipartite graph, where every vertex ranks its neighbors in an order of preference (with ties allowed) and let r be the worst rank used. A matching M is fair in G if it has maximum cardinality, subject to this, M matches the minimum number of vertices to rank r neighbors, subject to that, M matches the minimum number of vertices to rank (r-1) neighbors, and so on. We show an efficient combinatorial algorithm based on LP duality to compute a fair matching in G. We also show a scaling based algorithm for the fair b-matching problem.

Our two algorithms can be extended to solve other profile-based matching problems. In designing our combinatorial algorithm, we show how to solve a generalized version of the minimum weighted vertex cover problem in bipartite graphs, using a single-source shortest paths computation---this can be of independent interest.

BibTeX - Entry

@InProceedings{huang_et_al:LIPIcs:2013:4384,
  author =	{Chien-Chung Huang and Telikepalli Kavitha and Kurt Mehlhorn and Dimitrios Michail},
  title =	{{Fair Matchings and Related Problems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{339--350},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Anil Seth and Nisheeth K. Vishnoi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4384},
  URN =		{urn:nbn:de:0030-drops-43841},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.339},
  annote =	{Keywords: Matching with Preferences, Fairness and Rank-Maximality, Bipartite Vertex Cover, Linear Programming Duality, Complementary Slackness}
}

Keywords: Matching with Preferences, Fairness and Rank-Maximality, Bipartite Vertex Cover, Linear Programming Duality, Complementary Slackness
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Issue Date: 2013
Date of publication: 10.12.2013

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