We present a O(1)-approximate fully dynamic algorithm for the k-median and k-means problems on metric spaces with amortized update time O~(k) and worst-case query time O~(k2). We complement our theoretical analysis with the first in-depth experimental study for the dynamic k-median problem on general metrics, focusing on comparing our dynamic algorithm to the current state-of-the-art by Henzinger and Kale [ESA'20]. Finally, we also provide a lower bound for dynamic k-median which shows that any O(1)-approximate algorithm with O~(poly(k)) query time must have Ω~(k) amortized update time, even in the incremental setting.
@article{arxiv.2310.17420,
title = {Fully Dynamic $k$-Clustering in $\tilde O(k)$ Update Time},
author = {Sayan Bhattacharya and Martín Costa and Silvio Lattanzi and Nikos Parotsidis},
journal= {arXiv preprint arXiv:2310.17420},
year = {2023}
}