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Theory of Computing Systems

, Volume 63, Issue 8, pp 1849–1874 | Cite as

Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs

  • Itay Laish
  • Shay MozesEmail author
Article
  • 16 Downloads
Part of the following topical collections:
  1. Special Issue on Approximation and Online Algorithms (2017)

Abstract

Let G be a graph where each vertex is associated with a label. A vertex-labeled approximate distance oracle is a data structure that, given a vertex v and a label λ, returns a (1 + ε)-approximation of the distance from v to the closest vertex with label λ in G. Such an oracle is dynamic if it also supports label changes. In this paper we present three different dynamic approximate vertex-labeled distance oracles for planar graphs, all with polylogarithmic query and update times, and nearly linear space requirements. No such oracles were previously known.

Keywords

Planar graphs Approximate distance oracles Vertex labels Portals ε-cover 

Notes

Acknowledgements

We thank Paweł Gawrychowski and Oren Weimann for fruitful discussions.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Efi Arazi School of Computer ScienceThe Interdisciplinary Center HerzliyaHerzliyaIsrael

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