{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T19:17:05Z","timestamp":1771269425016,"version":"3.50.1"},"reference-count":0,"publisher":"TechForum Publishing Group","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. Comput. Data Sci."],"published-print":{"date-parts":[[2025,12,30]]},"abstract":"<jats:p>Fair clustering with \n(\n\u03b1\n,\n\u03b2\n)\n-proportionality constraints requires every cluster to satisfy lower and upper bounds on the representation of each sensitive group. Recent universal-coreset results enable scalable optimization by compressing the dataset into a small weighted subset that preserves constrained clustering costs simultaneously for all center sets and all feasible group-cardinality (coloring) constraints. In many applications, however, the sensitive attributes that motivate fairness constraints also require formal privacy protection, and releasing even a small coreset can leak membership and group information. We propose a modular framework for differentially private universal coresets for (\u03b1,\u03b2)-fair k-median and k-means in metric and Euclidean spaces. The framework consists of two stages: (i) construct a randomized \u03b7\/2-universal coreset via random sampling and reweighting; (ii) release a privatized coreset by perturbing only the weight vector using the Gaussian mechanism, followed by post-processing (nonnegativity and mass renormalization). We prove that the released summary is (\u03b5,\u03b4)-differentially private and, with high probability, preserves constrained costs for all (C,M) up to a multiplicative (1\u00b1\u03b7) factor plus an additive privacy term that depends on the metric diameter bound, coreset size, and an \u21132 weight-sensitivity parameter. We further extend the method to streaming via merge-and-reduce and analyze privacy under continual observation using advanced composition and amplification-by-subsampling. The resulting DP universal coresets allow multi-query fair clustering and interactive constraint tuning without repeated access to the raw sensitive dataset.<\/jats:p>","DOI":"10.71448\/bcds2564-2","type":"journal-article","created":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T18:14:07Z","timestamp":1771265647000},"page":"22-38","source":"Crossref","is-referenced-by-count":0,"title":["Differentially Private Universal Coresets for  ( \u03b1 , \u03b2 ) -Fair  k -Median and  k -Means Clustering"],"prefix":"10.71448","volume":"6","author":[{"name":"University of Agriculture Faisalabad (UAF), Pakistan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iftikhar","family":"Ahmad","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wang","family":"Zu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"name":"Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"52394","published-online":{"date-parts":[[2025,12,30]]},"container-title":["Bulletin of Computer and Data Sciences"],"original-title":[],"deposited":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T18:14:07Z","timestamp":1771265647000},"score":1,"resource":{"primary":{"URL":"https:\/\/bcds.ch\/differentially-private-universal-coresets-for-alphabeta-fair-k-median-and-k-means-clustering\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,30]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,12,30]]},"published-print":{"date-parts":[[2025,12,30]]}},"URL":"https:\/\/doi.org\/10.71448\/bcds2564-2","relation":{},"ISSN":["3072-2926"],"issn-type":[{"value":"3072-2926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,30]]}}}