{"paper":{"title":"Optimization Algorithms for Faster Computational Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","math.OC"],"primary_cat":"cs.CG","authors_text":"Yang Yuan, Zeyuan Allen-Zhu, Zhenyu Liao","submitted_at":"2014-12-02T18:15:46Z","abstract_excerpt":"We study two fundamental problems in computational geometry: finding the maximum inscribed ball (MaxIB) inside a bounded polyhedron defined by $m$ hyperplanes, and the minimum enclosing ball (MinEB) of a set of $n$ points, both in $d$-dimensional space. We improve the running time of iterative algorithms on\n  MaxIB from $\\tilde{O}(m d \\alpha^3 / \\varepsilon^3)$ to $\\tilde{O}(md + m \\sqrt{d} \\alpha / \\varepsilon)$, a speed-up up to $\\tilde{O}(\\sqrt{d} \\alpha^2 / \\varepsilon^2)$, and\n  MinEB from $\\tilde{O}(n d / \\sqrt{\\varepsilon})$ to $\\tilde{O}(nd + n \\sqrt{d} / \\sqrt{\\varepsilon})$, a speed-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1001","kind":"arxiv","version":3},"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"}