{"paper":{"title":"Better Tradeoffs for Exact Distance Oracles in Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Christian Wulff-Nilsen, Oren Weimann, Pawe{\\l} Gawrychowski, Shay Mozes","submitted_at":"2017-08-04T05:58:10Z","abstract_excerpt":"We present an $O(n^{1.5})$-space distance oracle for directed planar graphs that answers distance queries in $O(\\log n)$ time. Our oracle both significantly simplifies and significantly improves the recent oracle of Cohen-Addad, Dahlgaard and Wulff-Nilsen [FOCS 2017], which uses $O(n^{5/3})$-space and answers queries in $O(\\log n)$ time. We achieve this by designing an elegant and efficient point location data structure for Voronoi diagrams on planar graphs.\n  We further show a smooth tradeoff between space and query-time. For any $S\\in [n,n^2]$, we show an oracle of size $S$ that answers quer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01386","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"}