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oai:drops-oai.dagstuhl.de:15456 2024-03-06T10:55:20Z ddc:004 open_access

Near-Optimal Distance Oracles for Vertex-Labeled Planar Graphs Evald, Jacob Fredslund-Hansen, Viktor Wulff-Nilsen, Christian distance oracle vertex labels color distance oracle planar graph Given an undirected n-vertex planar graph G = (V,E,ω) with non-negative edge weight function ω:E → ℝ and given an assigned label to each vertex, a vertex-labeled distance oracle is a data structure which for any query consisting of a vertex u and a label λ reports the shortest path distance from u to the nearest vertex with label λ. We show that if there is a distance oracle for undirected n-vertex planar graphs with non-negative edge weights using s(n) space and with query time q(n), then there is a vertex-labeled distance oracle with Õ(s(n)) space and Õ(q(n)) query time. Using the state-of-the-art distance oracle of Long and Pettie [Long and Pettie, 2021], our construction produces a vertex-labeled distance oracle using n^{1+o(1)} space and query time Õ(1) at one extreme, Õ(n) space and n^o(1) query time at the other extreme, as well as such oracles for the full tradeoff between space and query time obtained in their paper. This is the first non-trivial exact vertex-labeled distance oracle for planar graphs and, to our knowledge, for any interesting graph class other than trees. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Jacob Evald and Viktor Fredslund-Hansen and Christian Wulff-Nilsen 2021 Is Part Of LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2021.23 urn:nbn:de:0030-drops-154566 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.23 eng https://creativecommons.org/licenses/by/4.0/legalcode