{"paper":{"title":"On the size of the largest empty box amidst a point set","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NA"],"primary_cat":"cs.CG","authors_text":"Aicke Hinrichs, Christoph Aistleitner, Daniel Rudolf","submitted_at":"2015-07-08T08:38:46Z","abstract_excerpt":"The problem of finding the largest empty axis-parallel box amidst a point configuration is a classical problem in computational geometry. It is known that the volume of the largest empty box is of asymptotic order $1/n$ for $n\\to\\infty$ and fixed dimension $d$. However, it is natural to assume that the volume of the largest empty box increases as $d$ gets larger. In the present paper we prove that this actually is the case: for every set of $n$ points in $[0, 1]^d$ there exists an empty box of volume at least $c_d n^{-1}$ , where $c_d \\to \\infty$ as $d\\to \\infty$. More precisely, $c_d$ is at l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02067","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"}