# Optimal Fully Dynamic k-Centers Clustering

@article{Bateni2021OptimalFD, title={Optimal Fully Dynamic k-Centers Clustering}, author={MohammadHossein Bateni and Hossein Esfandiari and Rajesh Jayaram and Vahab S. Mirrokni}, journal={ArXiv}, year={2021}, volume={abs/2112.07050} }

We present the first algorithm for fully dynamic k-centers clustering in an arbitrary metric space that maintains an optimal 2 + ǫ approximation in O(k · polylog(n,∆)) amortized update time. Here, n is an upper bound on the number of active points at any time, and ∆ is the aspect ratio of the data. Previously, the best known amortized update time was O(k · polylog(n,∆)), and is due to Chan, Gourqin, and Sozio [CGS18]. We demonstrate that the runtime of our algorithm is optimal up to polylog(n…

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