{"paper":{"title":"Depth Distribution in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Javiel Rojas-Ledesma, J\\'er\\'emy Barbay, Pablo P\\'erez-Lantero","submitted_at":"2017-05-29T02:31:33Z","abstract_excerpt":"Motivated by the analysis of range queries in databases, we introduce the computation of the Depth Distribution of a set $\\mathcal{B}$ of axis aligned boxes, whose computation generalizes that of the Klee's Measure and of the Maximum Depth. In the worst case over instances of fixed input size $n$, we describe an algorithm of complexity within $O({n^\\frac{d+1}{2}\\log n})$, using space within $O({n\\log n})$, mixing two techniques previously used to compute the Klee's Measure. We refine this result and previous results on the Klee's Measure and the Maximum Depth for various measures of difficulty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10022","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"}