Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Fomin, Fedor V.; Golovach, Petr A.; Jaffke, Lars; Philip, Geevarghese; Sagunov, Danil https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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URN: urn:nbn:de:0030-drops-133706
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Diverse Pairs of Matchings

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Abstract

We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph G and an integer k, ask whether G has two (maximum/perfect) matchings whose symmetric difference is at least k. Diverse Pair of Matchings (asking for two not necessarily maximum or perfect matchings) is NP-complete on general graphs if k is part of the input, and we consider two restricted variants. First, we show that on bipartite graphs, the problem is polynomial-time solvable, and second we show that Diverse Pair of Maximum Matchings is FPT parameterized by k. We round off the work by showing that Diverse Pair of Matchings has a kernel on 𝒪(k²) vertices.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2020:13370,
  author =	{Fedor V. Fomin and Petr A. Golovach and Lars Jaffke and Geevarghese Philip and Danil Sagunov},
  title =	{{Diverse Pairs of Matchings}},
  booktitle =	{31st International Symposium on Algorithms and Computation (ISAAC 2020)},
  pages =	{26:1--26:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-173-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{181},
  editor =	{Yixin Cao and Siu-Wing Cheng and Minming Li},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/13370},
  URN =		{urn:nbn:de:0030-drops-133706},
  doi =		{10.4230/LIPIcs.ISAAC.2020.26},
  annote =	{Keywords: Matching, Solution Diversity, Fixed-Parameter Tractability}
}

Keywords: Matching, Solution Diversity, Fixed-Parameter Tractability
Seminar: 31st International Symposium on Algorithms and Computation (ISAAC 2020)
Issue date: 2020
Date of publication: 04.12.2020


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