Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH Schloss Dagstuhl - Leibniz-Zentrum für Informatik GmbH scholarly article en Arar, Moab; Chechik, Shiri; Cohen, Sarel; Stein, Cliff; Wajc, David https://www.dagstuhl.de/lipics License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
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Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms

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Abstract

We present a simple randomized reduction from fully-dynamic integral matching algorithms to fully-dynamic "approximately-maximal" fractional matching algorithms. Applying this reduction to the recent fractional matching algorithm of Bhattacharya, Henzinger, and Nanongkai (SODA 2017), we obtain a novel result for the integral problem. Specifically, our main result is a randomized fully-dynamic (2+epsilon)-approximate integral matching algorithm with small polylog worst-case update time. For the (2+epsilon)-approximation regime only a fractional fully-dynamic (2+epsilon)-matching algorithm with worst-case polylog update time was previously known, due to Bhattacharya et al. (SODA 2017). Our algorithm is the first algorithm that maintains approximate matchings with worst-case update time better than polynomial, for any constant approximation ratio. As a consequence, we also obtain the first constant-approximate worst-case polylogarithmic update time maximum weight matching algorithm.

BibTeX - Entry

@InProceedings{arar_et_al:LIPIcs:2018:9011,
  author =	{Moab Arar and Shiri Chechik and Sarel Cohen and Cliff Stein and David Wajc},
  title =	{{Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9011},
  URN =		{urn:nbn:de:0030-drops-90112},
  doi =		{10.4230/LIPIcs.ICALP.2018.7},
  annote =	{Keywords: Dynamic, Worst-case, Maximum Matching, Maximum Weight Matching}
}

Keywords: Dynamic, Worst-case, Maximum Matching, Maximum Weight Matching
Seminar: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue date: 2018
Date of publication: 04.07.2018


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