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.

OriginalsprogEngelsk
Titel32nd International Symposium on Algorithms and Computation, ISAAC 2021
RedaktørerHee-Kap Ahn, Kunihiko Sadakane
Antal sider14
ForlagSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Publikationsdato2021
Artikelnummer23
ISBN (Elektronisk)9783959772143
DOI
StatusUdgivet - 2021
Begivenhed32nd International Symposium on Algorithms and Computation, ISAAC 2021 - Fukuoka, Japan
Varighed: 6 dec. 20218 dec. 2021

Konference

Konference32nd International Symposium on Algorithms and Computation, ISAAC 2021
LandJapan
ByFukuoka
Periode06/12/202108/12/2021
NavnLeibniz International Proceedings in Informatics, LIPIcs
Vol/bind212
ISSN1868-8969

ID: 291367568