Approximate shortest path queries using Voronoi duals

Shinichi Honiden, Michael E. Houle, Christian Sommer, Martin Wolff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

We propose an approximation method to answer point-to-point shortest path queries in undirected edge-weighted graphs, based on random sampling and Voronoi duals. We compute a simplification of the graph by selecting nodes independently at random with probability p. Edges are generated as the Voronoi dual of the original graph, using the selected nodes as Voronoi sites. This overlay graph allows for fast computation of approximate shortest paths for general, undirected graphs. The time-quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths as well as experimental results. The theoretical worst-case approximation ratio is bounded by a logarithmic factor. Experiments show that our approximation method based on Voronoi duals has extremely fast preprocessing time and efficiently computes reasonably short paths.

Original languageEnglish
Title of host publicationTransactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering
Pages28-53
Number of pages26
DOIs
Publication statusPublished - 2010 Dec 13
Externally publishedYes
EventInternational Symposium on Voronoi Diagrams 2009 - Copenhagen, Denmark
Duration: 2009 Jun 232009 Jun 26

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6290 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

OtherInternational Symposium on Voronoi Diagrams 2009
CountryDenmark
CityCopenhagen
Period09/6/2309/6/26

Fingerprint

Voronoi
Shortest path
Query
Sampling
Approximation Methods
Graph in graph theory
Experiments
Random Sampling
Path Length
Weighted Graph
Approximation
Vertex of a graph
Overlay
Undirected Graph
Simplification
Preprocessing
Logarithmic
Trade-offs
Experimental Results
Experiment

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Honiden, S., Houle, M. E., Sommer, C., & Wolff, M. (2010). Approximate shortest path queries using Voronoi duals. In Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering (pp. 28-53). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6290 LNCS). https://doi.org/10.1007/978-3-642-16007-3_2

Approximate shortest path queries using Voronoi duals. / Honiden, Shinichi; Houle, Michael E.; Sommer, Christian; Wolff, Martin.

Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering. 2010. p. 28-53 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6290 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Honiden, S, Houle, ME, Sommer, C & Wolff, M 2010, Approximate shortest path queries using Voronoi duals. in Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6290 LNCS, pp. 28-53, International Symposium on Voronoi Diagrams 2009, Copenhagen, Denmark, 09/6/23. https://doi.org/10.1007/978-3-642-16007-3_2
Honiden S, Houle ME, Sommer C, Wolff M. Approximate shortest path queries using Voronoi duals. In Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering. 2010. p. 28-53. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-16007-3_2
Honiden, Shinichi ; Houle, Michael E. ; Sommer, Christian ; Wolff, Martin. / Approximate shortest path queries using Voronoi duals. Transactions on Computational Science IX - Special Issue on Voronoi Diagrams in Science and Engineering. 2010. pp. 28-53 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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