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.2021.25
URN: urn:nbn:de:0030-drops-154586
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/15458/
Go to the corresponding LIPIcs Volume Portal

Fredslund-Hansen, Viktor ; Mozes, Shay ; Wulff-Nilsen, Christian

Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs

pdf-format:
LIPIcs-ISAAC-2021-25.pdf (0.8 MB)

Abstract

We present a truly subquadratic size distance oracle for reporting, in constant time, the exact shortest-path distance between any pair of vertices of an undirected, unweighted planar graph G. For any ε > 0, our distance oracle requires O(n^{5/3+ε}) space and is capable of answering shortest-path distance queries exactly for any pair of vertices of G in worst-case time O(log (1/ε)). Previously no truly sub-quadratic size distance oracles with constant query time for answering exact shortest paths distance queries existed.

BibTeX - Entry

@InProceedings{fredslundhansen_et_al:LIPIcs.ISAAC.2021.25,
  author =	{Fredslund-Hansen, Viktor and Mozes, Shay and Wulff-Nilsen, Christian},
  title =	{{Truly Subquadratic Exact Distance Oracles with Constant Query Time for Planar Graphs}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{25:1--25:12},
  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/2021/15458},
  URN =		{urn:nbn:de:0030-drops-154586},
  doi =		{10.4230/LIPIcs.ISAAC.2021.25},
  annote =	{Keywords: distance oracle, planar graph, shortest paths, subquadratic}
}

Keywords: distance oracle, planar graph, shortest paths, subquadratic
Collection: 32nd International Symposium on Algorithms and Computation (ISAAC 2021)
Issue Date: 2021
Date of publication: 30.11.2021

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI