{"paper":{"title":"$k$-Center Clustering with Outliers in the MPC and Streaming Model","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Leyla Biabani, Mark de Berg, Morteza Monemizadeh","submitted_at":"2023-02-24T18:46:27Z","abstract_excerpt":"Given a point set $P \\subseteq X$ of size $n$ in a metric space $(X,dist)$ of doubling dimension $d$ and two parameters $k \\in N$ and $z \\in N$, the $k$-center problem with $z$ outliers asks to return a set $C^\\ast \\subseteq X$ of $k$ centers such that the maximum distance of all but $z$ points of $P$ to their nearest center in $C^\\ast$ is minimized. An $(\\epsilon,k,z)$-coreset for this problem is a weighted point set $P^*$ such that an optimal solution for the $k$-center problem with $z$ outliers on $P^*$ gives a $(1\\pm\\epsilon)$-approximation for the $k$-center problem with $z$ outliers on $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.12811","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/2302.12811/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"}