Efficient Dynamic Approximate Distance Oracles for Vertex-Labeled Planar Graphs

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 als...

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Bibliographic Details
Published in:Theory of computing systems Vol. 63; no. 8; pp. 1849 - 1874
Main Authors: Laish, Itay, Mozes, Shay
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2019
Springer Nature B.V
Subjects:
Computer Science
Data structures
Graphs
Special Issue on Approximation and Online Algorithms
Theory of Computation
cover
Approximate distance oracles
Vertex labels
Portals
Planar graphs
ISSN:1432-4350, 1433-0490
Online Access:Get full text
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Summary: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.
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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-019-09949-5