License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ISAAC.2021.23
URN: urn:nbn:de:0030-drops-154566
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15456/
Evald, Jacob ;
Fredslund-Hansen, Viktor ;
Wulff-Nilsen, Christian
Near-Optimal Distance Oracles for Vertex-Labeled Planar Graphs
Abstract
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.
BibTeX - Entry
@InProceedings{evald_et_al:LIPIcs.ISAAC.2021.23,
author = {Evald, Jacob and Fredslund-Hansen, Viktor and Wulff-Nilsen, Christian},
title = {{Near-Optimal Distance Oracles for Vertex-Labeled Planar Graphs}},
booktitle = {32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
pages = {23:1--23:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-214-3},
ISSN = {1868-8969},
year = {2021},
volume = {212},
editor = {Ahn, Hee-Kap and Sadakane, Kunihiko},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15456},
URN = {urn:nbn:de:0030-drops-154566},
doi = {10.4230/LIPIcs.ISAAC.2021.23},
annote = {Keywords: distance oracle, vertex labels, color distance oracle, planar graph}
}
Keywords: |
|
distance oracle, vertex labels, color distance oracle, planar graph |
Collection: |
|
32nd International Symposium on Algorithms and Computation (ISAAC 2021) |
Issue Date: |
|
2021 |
Date of publication: |
|
30.11.2021 |