{"paper":{"title":"Adaptive Computation of the Klee's Measure in High Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Javiel Rojas-Ledesma, J\\'er\\'emy Barbay, Pablo P\\'erez-Lantero","submitted_at":"2015-05-12T01:55:25Z","abstract_excerpt":"The KLEE'S MESURE of $n$ axis-parallel boxes in $\\mathbb{R}^d$ is the volume of their union. It can be computed in time within $O(n^{d/2})$ in the worst case. We describe three techniques to boost its computation: one based on some type of \"degeneracy'' of the input, and two ones on the inherent \"easiness'' of the structure of the input. The first technique benefits from instances where the MAXIMA of the input is of small size $h$, and yields a solution running in time within $O(n\\log^{2d-2}{h}+ h^{d/2}) \\subseteq O(n^{d/2}$). The second technique takes advantage of instances where no $d$-dime"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02855","kind":"arxiv","version":2},"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"}