{"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/individual-fairness-for-k-clustering","title":"Individual Fairness for $k$-Clustering","arxiv_id":"2002.06742","date":"2020-02-17","proceeding":null,"authors":["Sepideh Mahabadi","Ali Vakilian"],"abstract":"We give a local search based algorithm for $k$-median and $k$-means (and more generally for any $k$-clustering with $\\ell_p$ norm cost function) from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\\in P$ expects to have a center within radius $r(x)$. An individually fair clustering provides such a guarantee for every point $x\\in P$. This notion of fairness was introduced in [Jung et al., 2019] where they showed how to get an approximately feasible $k$-clustering with respect to this fairness condition. In this work, we show how to get a bicriteria approximation for fair $k$-clustering: The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor). Further, we complement our theoretical bounds with empirical evaluation.","url_abs":"https://arxiv.org/abs/2002.06742v2","url_pdf":"https://arxiv.org/pdf/2002.06742v2.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":"individual-fairness-for-k-clustering","repo_url":"https://github.com/jayeshchoudhari/coresetindividualfairness","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"fairness","task_name":"Fairness"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.06742","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}