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DOI: 10.4230/LIPIcs.ICALP.2018.7
Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms

Authors: Moab Arar, Shiri Chechik, Sarel Cohen, Cliff Stein, and David Wajc

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

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.
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Moab Arar, Shiri Chechik, Sarel Cohen, Cliff Stein, and David Wajc. Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{arar_et_al:LIPIcs.ICALP.2018.7,
  author =	{Arar, Moab and Chechik, Shiri and Cohen, Sarel and Stein, Cliff and Wajc, David},
  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 =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.7},
  URN =		{urn:nbn:de:0030-drops-90112},
  doi =		{10.4230/LIPIcs.ICALP.2018.7},
  annote =	{Keywords: Dynamic, Worst-case, Maximum Matching, Maximum Weight Matching}
}
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