{"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/a-composable-coreset-for-k-center-in-doubling","title":"A Composable Coreset for k-Center in Doubling Metrics","arxiv_id":"1902.01896","date":"2019-02-05","proceeding":null,"authors":["Sepideh Aghamolaei","Mohammad Ghodsi"],"abstract":"A set of points $P$ in a metric space and a constant integer $k$ are given. The $k$-center problem finds $k$ points as centers among $P$, such that the maximum distance of any point of $P$ to their closest centers $(r)$ is minimized. Doubling metrics are metric spaces in which for any $r$, a ball of radius $r$ can be covered using a constant number of balls of radius $r/2$. Fixed dimensional Euclidean spaces are doubling metrics. The lower bound on the approximation factor of $k$-center is $1.822$ in Euclidean spaces, however, $(1+\\epsilon)$-approximation algorithms with exponential dependency on $\\frac{1}{\\epsilon}$ and $k$ exist. For a given set of sets $P_1,\\ldots,P_L$, a composable coreset independently computes subsets $C_1\\subset P_1, \\ldots, C_L\\subset P_L$, such that $\\cup_{i=1}^L C_i$ contains an approximation of a measure of the set $\\cup_{i=1}^L P_i$. We introduce a $(1+\\epsilon)$-approximation composable coreset for $k$-center, which in doubling metrics has size sublinear in $|P|$. This results in a $(2+\\epsilon)$-approximation algorithm for $k$-center in MapReduce with a constant number of rounds in doubling metrics for any $\\epsilon>0$ and sublinear communications, which is based on parametric pruning. We prove the exponential nature of the trade-off between the number of centers $(k)$ and the radius $(r)$, and give a composable coreset for a related problem called dual clustering. Also, we give a new version of the parametric pruning algorithm with $O(\\frac{nk}{\\epsilon})$ running time, $O(n)$ space and $2+\\epsilon$ approximation factor for metric $k$-center.","url_abs":"https://arxiv.org/abs/1902.01896v2","url_pdf":"https://arxiv.org/pdf/1902.01896v2.pdf","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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-composable-coreset-for-k-center-in-doubling","repo_url":"https://gitlab.com/sepid014/composable-coreset-for-k-center","is_official":1,"mentioned_in_paper":0,"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}