{"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-simple-randomized-o-n-log-n-time-closest","title":"A Simple Randomized $O(n \\log n)$--Time Closest-Pair Algorithm in Doubling Metrics","arxiv_id":"2004.05883","date":"2020-04-13","proceeding":null,"authors":["Anil Maheshwari","Wolfgang Mulzer","Michiel Smid"],"abstract":"Consider a metric space $(P,dist)$ with $N$ points whose doubling dimension is a constant. We present a simple, randomized, and recursive algorithm that computes, in $O(N \\log N)$ expected time, the closest-pair distance in $P$. To generate recursive calls, we use previous results of Har-Peled and Mendel, and Abam and Har-Peled for computing a sparse annulus that separates the points in a balanced way.","url_abs":"https://arxiv.org/abs/2004.05883v1","url_pdf":"https://arxiv.org/pdf/2004.05883v1.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-simple-randomized-o-n-log-n-time-closest","repo_url":"https://github.com/ThangMinhCao/closest-pair-doubling","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"a-simple-randomized-o-n-log-n-time-closest","repo_url":"https://github.com/ThangMinhCao/closestpairdoubling","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}