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Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms

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

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ACM Subject Classification
  • Theory of computation → Dynamic graph algorithms
Keywords
  • Dynamic
  • Worst-case
  • Maximum Matching
  • Maximum Weight Matching

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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.

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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) https://doi.org/10.4230/LIPIcs.ICALP.2018.7

Author Details

Moab Arar
  • Tel Aviv University, Tel Aviv, Israel
Shiri Chechik
  • Tel Aviv University, Tel Aviv, Israel
Sarel Cohen
  • Tel Aviv University, Tel Aviv, Israel
Cliff Stein
  • Columbia University, New York, USA
David Wajc
  • Carnegie Mellon University, Pittsburgh, USA

Funding

  • Stein, Cliff: Supported in part by NSF grant CCF-1421161.
  • Wajc, David: Supported in part by NSF grants CCF-1527110, CCF-1618280 and NSF CAREER award CCF-1750808.

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