{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/fully-dynamic-k-clustering-in-tilde-o-k","title":"Fully Dynamic $k$-Clustering in $\\tilde O(k)$ Update Time","arxiv_id":null,"date":"2023-09-21","proceeding":"NeurIPS 2023 11","authors":[],"abstract":"We present a $O(1)$-approximate fully dynamic algorithm for the $k$-median and $k$-means problems on metric spaces with amortized update time $\\tilde O(k)$ and worst-case query time $\\tilde O(k^2)$. 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 $\\tilde O(\\text{poly}(k))$ query time must have $\\tilde \\Omega(k)$ amortized update time, even in the incremental setting.","url_abs":"https://openreview.net/forum?id=dnGEPkmnzO","url_pdf":"https://openreview.net/pdf?id=dnGEPkmnzO","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"fully-dynamic-k-clustering-in-tilde-o-k","repo_url":"https://github.com/martin-costa/neurips23-dynamic-k-clustering","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}