{"paper":{"title":"Efficient Vertex-Label Distance Oracles for Planar Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Eyal E. Skop, Shay Mozes","submitted_at":"2015-04-18T07:24:00Z","abstract_excerpt":"We consider distance queries in vertex-labeled planar graphs. For any fixed $0 < \\epsilon \\leq 1/2$ we show how to preprocess a directed planar graph with vertex labels and arc lengths into a data structure that answers queries of the following form. Given a vertex $u$ and a label $\\lambda$ return a $(1+\\epsilon)$-approximation of the distance from $u$ to its closest vertex with label $\\lambda$. For a directed planar graph with $n$ vertices, such that the ratio of the largest to smallest arc length is bounded by $N$, the preprocessing time is $O(\\epsilon^{-2}n\\lg^{3}{n}\\lg(nN))$, the data stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.04690","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"}