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

11/17/2017

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by   Moab Arar, et al.

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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 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.