{"paper":{"title":"Almost Optimal Distance Oracles for Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Oren Weimann, Panagiotis Charalampopoulos, Pawe{\\l} Gawrychowski, Shay Mozes","submitted_at":"2018-11-05T08:37:57Z","abstract_excerpt":"We present new tradeoffs between space and query-time for exact distance oracles in directed weighted planar graphs. These tradeoffs are almost optimal in the sense that they are within polylogarithmic, sub-polynomial or arbitrarily small polynomial factors from the na\\\"{\\i}ve linear space, constant query-time lower bound. These tradeoffs include: (i) an oracle with space $\\tilde{O}(n^{1+\\epsilon})$ and query-time $\\tilde{O}(1)$ for any constant $\\epsilon>0$, (ii) an oracle with space $\\tilde{O}(n)$ and query-time $\\tilde{O}(n^{\\epsilon})$ for any constant $\\epsilon>0$, and (iii) an oracle wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01551","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"}