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arXiv · 1711.06625

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

Moab Arar·Shiri Chechik·Sarel Cohen·Cliff Stein·David Wajc
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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 $(2+ε)$-approximate integral matching algorithm with small polylog worst-case update time. For the $(2+ε)$-approximation regime only a \emph{fractional} fully-dynamic $(2+ε)$-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, David Wajc. 2018-02-27. Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal Fractional Algorithms. https://arxiv.org/abs/1711.06625

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