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.2020.25
URN: urn:nbn:de:0030-drops-132668
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/13266/
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Kavitha, Telikepalli

Min-Cost Popular Matchings

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LIPIcs-FSTTCS-2020-25.pdf (0.5 MB)

Abstract

Let G = (A ∪ B, E) be a bipartite graph on n vertices where every vertex ranks its neighbors in a strict order of preference. A matching M in G is popular if there is no matching N such that vertices that prefer N to M outnumber those that prefer M to N. Popular matchings always exist in G since every stable matching is popular. Thus it is easy to find a popular matching in G - however it is NP-hard to compute a min-cost popular matching in G when there is a cost function on the edge set; moreover it is NP-hard to approximate this to any multiplicative factor. An O^*(2ⁿ) algorithm to compute a min-cost popular matching in G follows from known results. Here we show:
- an algorithm with running time O^*(2^{n/4}) ≈ O^*(1.19ⁿ) to compute a min-cost popular matching;
- assume all edge costs are non-negative - then given ε > 0, a randomized algorithm with running time poly(n,1/(ε)) to compute a matching M such that cost(M) is at most twice the optimal cost and with high probability, the fraction of all matchings more popular than M is at most 1/2+ε.

BibTeX - Entry

@InProceedings{kavitha:LIPIcs:2020:13266,
  author =	{Telikepalli Kavitha},
  title =	{{Min-Cost Popular Matchings}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{25:1--25:17},
  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 =		{https://drops.dagstuhl.de/opus/volltexte/2020/13266},
  URN =		{urn:nbn:de:0030-drops-132668},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.25},
  annote =	{Keywords: Bipartite graphs, Stable matchings, Dual certificates}
}

Keywords: Bipartite graphs, Stable matchings, Dual certificates
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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