{"paper":{"title":"Orthogonal Range Searching on the RAM, Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Kasper Green Larsen, Mihai Patrascu, Timothy M. Chan","submitted_at":"2011-03-28T23:32:35Z","abstract_excerpt":"We present several new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model for points in rank space:\n  ** We present two data structures for 2-d orthogonal range emptiness. The first achieves O(n lglg n) space and O(lglg n) query time. This improves the previous results by Alstrup, Brodal, and Rauhe(FOCS'00), with O(n lg^eps n) space and O(lglg n) query time, or with O(nlglg n) space and O(lg^2 lg n) query time. Our second data structure uses O(n) space and answers queries in O(lg^eps n)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5510","kind":"arxiv","version":1},"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"}