Dynamic Matching: Reducing Integral Algorithms to Approximately-Maximal
Fractional Algorithms
release_ibtgntip25dbretoruaww7nqby
by
Moab Arar, Shiri Chechik, Sarel Cohen, Cliff Stein, David Wajc
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+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. As a consequence, we also obtain the first
constant-approximate worst-case polylogarithmic update time maximum weight
matching algorithm.
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