{"paper":{"title":"Fast, precise and dynamic distance queries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lee-Ad Gottlieb, Liam Roditty, Moshe Lewenstein, Tsvi Kopelowitz, Yair Bartal","submitted_at":"2010-08-09T10:21:33Z","abstract_excerpt":"We present an approximate distance oracle for a point set S with n points and doubling dimension {\\lambda}. For every {\\epsilon}>0, the oracle supports (1+{\\epsilon})-approximate distance queries in (universal) constant time, occupies space [{\\epsilon}^{-O({\\lambda})} + 2^{O({\\lambda} log {\\lambda})}]n, and can be constructed in [2^{O({\\lambda})} log3 n + {\\epsilon}^{-O({\\lambda})} + 2^{O({\\lambda} log {\\lambda})}]n expected time. This improves upon the best previously known constructions, presented by Har-Peled and Mendel. Furthermore, the oracle can be made fully dynamic with expected O(1) q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1480","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"}