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.ESA.2018.53
URN: urn:nbn:de:0030-drops-95169
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9516/
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Korenwein, Viatcheslav ; Nichterlein, André ; Niedermeier, Rolf ; Zschoche, Philipp

Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments

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LIPIcs-ESA-2018-53.pdf (0.5 MB)

Abstract

Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For n-vertex and m-edge graphs, the best known algorithms run in O~(m sqrt{n}) time. We build on recent theoretical work focusing on linear-time data reduction rules for finding maximum-cardinality matchings and complement the theoretical results by presenting and analyzing (thereby employing the kernelization methodology of parameterized complexity analysis) linear-time data reduction rules for the positive-integer-weighted case. Moreover, we experimentally demonstrate that these data reduction rules provide significant speedups of the state-of-the art implementation for computing matchings in real-world graphs: the average speedup is 3800% in the unweighted case and "just" 30% in the weighted case.

BibTeX - Entry

@InProceedings{korenwein_et_al:LIPIcs:2018:9516,
  author =	{Viatcheslav Korenwein and Andr{\'e} Nichterlein and Rolf Niedermeier and Philipp Zschoche},
  title =	{{Data Reduction for Maximum Matching on Real-World Graphs: Theory and Experiments}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{53:1--53:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Yossi Azar and Hannah Bast and Grzegorz Herman},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9516},
  URN =		{urn:nbn:de:0030-drops-95169},
  doi =		{10.4230/LIPIcs.ESA.2018.53},
  annote =	{Keywords: Maximum-cardinality matching, maximum-weight matching, linear-time algorithms, preprocessing, kernelization, parameterized complexity analysis}
}

Keywords: Maximum-cardinality matching, maximum-weight matching, linear-time algorithms, preprocessing, kernelization, parameterized complexity analysis
Collection: 26th Annual European Symposium on Algorithms (ESA 2018)
Issue Date: 2018
Date of publication: 14.08.2018

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