{"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/consistent-k-median-simpler-better-and-robust","title":"Consistent $k$-Median: Simpler, Better and Robust","arxiv_id":"2008.06101","date":"2020-08-13","proceeding":null,"authors":["Xiangyu Guo","Janardhan Kulkarni","Shi Li","Jiayi Xian"],"abstract":"In this paper we introduce and study the online consistent $k$-clustering with outliers problem, generalizing the non-outlier version of the problem studied in [Lattanzi-Vassilvitskii, ICML17]. We show that a simple local-search based online algorithm can give a bicriteria constant approximation for the problem with $O(k^2 \\log^2 (nD))$ swaps of medians (recourse) in total, where $D$ is the diameter of the metric. When restricted to the problem without outliers, our algorithm is simpler, deterministic and gives better approximation ratio and recourse, compared to that of [Lattanzi-Vassilvitskii, ICML17].","url_abs":"https://arxiv.org/abs/2008.06101v1","url_pdf":"https://arxiv.org/pdf/2008.06101v1.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":"abstracts"},"code_links":[{"paper_slug":"consistent-k-median-simpler-better-and-robust","repo_url":"https://github.com/xyguo/OnlineKZMedian","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2008.06101","atlas_url":"https://app.syntology.ai/?focus=2008.06101","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}