Near-Optimal Distance Oracles for Vertex-Labeled Planar Graphs
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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))1 space and Õ(q(n)) query time. Using the state-of-the-art distance oracle of Long and Pettie [12], our construction produces a vertex-labeled distance oracle using n1+o(1) space and query time Õ(1) at one extreme, Õ(n) space and no(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.
Originalsprog | Engelsk |
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Titel | 32nd International Symposium on Algorithms and Computation, ISAAC 2021 |
Redaktører | Hee-Kap Ahn, Kunihiko Sadakane |
Antal sider | 14 |
Forlag | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
Publikationsdato | 2021 |
Artikelnummer | 23 |
ISBN (Elektronisk) | 9783959772143 |
DOI | |
Status | Udgivet - 2021 |
Begivenhed | 32nd International Symposium on Algorithms and Computation, ISAAC 2021 - Fukuoka, Japan Varighed: 6 dec. 2021 → 8 dec. 2021 |
Konference
Konference | 32nd International Symposium on Algorithms and Computation, ISAAC 2021 |
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Land | Japan |
By | Fukuoka |
Periode | 06/12/2021 → 08/12/2021 |
Navn | Leibniz International Proceedings in Informatics, LIPIcs |
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Vol/bind | 212 |
ISSN | 1868-8969 |
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