{"paper":{"title":"New Approximation Algorithms for Minimum Enclosing Convex Shapes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"cs.CG","authors_text":"(2) Purdue University, (3) University of Alberta), Ankan Saha (1), S.V.N. Vishwanathan (2), Xinhua Zhang (3) ((1) University of Chicago","submitted_at":"2009-09-05T23:24:32Z","abstract_excerpt":"Given $n$ points in a $d$ dimensional Euclidean space, the Minimum Enclosing Ball (MEB) problem is to find the ball with the smallest radius which contains all $n$ points. We give a $O(nd\\Qcal/\\sqrt{\\epsilon})$ approximation algorithm for producing an enclosing ball whose radius is at most $\\epsilon$ away from the optimum (where $\\Qcal$ is an upper bound on the norm of the points). This improves existing results using \\emph{coresets}, which yield a $O(nd/\\epsilon)$ greedy algorithm. Finding the Minimum Enclosing Convex Polytope (MECP) is a related problem wherein a convex polytope of a fixed s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.1062","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}