{"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/improved-approximation-and-scalability-for","title":"Improved Approximation and Scalability for Fair Max-Min Diversification","arxiv_id":"2201.06678","date":"2022-01-18","proceeding":null,"authors":["Raghavendra Addanki","Andrew McGregor","Alexandra Meliou","Zafeiria Moumoulidou"],"abstract":"Given an $n$-point metric space $(\\mathcal{X},d)$ where each point belongs to one of $m=O(1)$ different categories or groups and a set of integers $k_1, \\ldots, k_m$, the fair Max-Min diversification problem is to select $k_i$ points belonging to category $i\\in [m]$, such that the minimum pairwise distance between selected points is maximized. The problem was introduced by Moumoulidou et al. [ICDT 2021] and is motivated by the need to down-sample large data sets in various applications so that the derived sample achieves a balance over diversity, i.e., the minimum distance between a pair of selected points, and fairness, i.e., ensuring enough points of each category are included. We prove the following results: 1. We first consider general metric spaces. We present a randomized polynomial time algorithm that returns a factor $2$-approximation to the diversity but only satisfies the fairness constraints in expectation. Building upon this result, we present a $6$-approximation that is guaranteed to satisfy the fairness constraints up to a factor $1-\\epsilon$ for any constant $\\epsilon$. We also present a linear time algorithm returning an $m+1$ approximation with exact fairness. The best previous result was a $3m-1$ approximation. 2. We then focus on Euclidean metrics. We first show that the problem can be solved exactly in one dimension. For constant dimensions, categories and any constant $\\epsilon>0$, we present a $1+\\epsilon$ approximation algorithm that runs in $O(nk) + 2^{O(k)}$ time where $k=k_1+\\ldots+k_m$. We can improve the running time to $O(nk)+ poly(k)$ at the expense of only picking $(1-\\epsilon) k_i$ points from category $i\\in [m]$. Finally, we present algorithms suitable to processing massive data sets including single-pass data stream algorithms and composable coresets for the distributed processing.","url_abs":"https://arxiv.org/abs/2201.06678v1","url_pdf":"https://arxiv.org/pdf/2201.06678v1.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":"improved-approximation-and-scalability-for","repo_url":"https://github.com/yhwang1990/code-fdm","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2201.06678","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}