Fast and compact oracles for approximate distances in planar graphs

Authors:
Laurent Flindt Muller;Martin Zachariasen
Affiliations:
Transvision, Copenhagen, Denmark;Department of Computer Science, University of Copenhagen, Copenhagen, Denmark
Venue:
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Year:
2007

Citing 9
Cited 5

Introduction to algorithms

Introduction to algorithms
Preprocessing an undirected planar network to enable fast approximate distance queries

SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Planar Graphs, Negative Weight Edges, Shortest Paths, and Near Linear Time

FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Distance labeling in graphs

Journal of Algorithms
Compact oracles for reachability and approximate distances in planar digraphs

Journal of the ACM (JACM)
Approximate distance oracles

Journal of the ACM (JACM)
Computing the shortest path: A search meets graph theory

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Engineering highway hierarchies

ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Highway hierarchies hasten exact shortest path queries

ESA'05 Proceedings of the 13th annual European conference on Algorithms

Engineering Route Planning Algorithms

Algorithmics of Large and Complex Networks
Customizable route planning

SEA'11 Proceedings of the 10th international conference on Experimental algorithms
Linear-space approximate distance oracles for planar, bounded-genus and minor-free graphs

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Engineering highway hierarchies

Journal of Experimental Algorithmics (JEA)
Shortest-path queries in static networks

ACM Computing Surveys (CSUR)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present an experimental evaluation of an approximate distance oracle recently suggested by Thorup [1] for undirected planar graphs. The oracle uses the existence of graph separators for planar graphs, discovered by Lipton and Tarjan [2], in order to divide the graph into smaller subgraphs. For a planar graph with n nodes, the algorithmic variant considered uses O(n(log n)3/Ɛ) preprocessing time and O(n(log n)2/Ɛ) space to answer factor (1 + Ɛ) distance queries in O((log n)2/Ɛ) time. By performing experiments on randomly generated planar graphs and on planar graphs derived from real world road networks, we investigate some key characteristics of the oracle, such as preprocessing time, query time, precision, and characteristics related to the underlying data structure, including space consumption. For graphs with one million nodes, the average query time is less than 20µs.