{"paper":{"title":"Coresets for Robust Clustering via Black-box Reductions to Vanilla Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jianing Lou, Shaofeng H.-C. Jiang","submitted_at":"2025-02-11T16:14:53Z","abstract_excerpt":"We devise $\\epsilon$-coresets for robust $(k,z)$-Clustering with $m$ outliers through black-box reductions to vanilla case. Given an $\\epsilon$-coreset construction for vanilla clustering with size $N$, we construct coresets of size $N\\cdot \\mathrm{poly}\\log(km\\epsilon^{-1}) + O_z\\left(\\min\\{km\\epsilon^{-1}, m\\epsilon^{-2z}\\log^z(km\\epsilon^{-1}) \\}\\right)$ for various metric spaces, where $O_z$ hides $2^{O(z\\log z)}$ factors. This increases the size of the vanilla coreset by a small multiplicative factor of $\\mathrm{poly}\\log(km\\epsilon^{-1})$, and the additive term is up to a $(\\epsilon^{-1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07669","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.07669/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}