Approximate shortest path queries in graphs 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 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 publication6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009
Pages53-62
Number of pages10
DOIs
Publication statusPublished - 2009 Dec 1
Externally publishedYes
Event6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 - Copenhagen, Denmark
Duration: 2009 Jun 232009 Jun 26

Other

Other6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009
CountryDenmark
CityCopenhagen
Period09/6/2309/6/26

Fingerprint

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

Keywords

  • Approximation
  • Distance oracle
  • Graph Voronoi diagram
  • Shortest path

ASJC Scopus subject areas

  • Information Systems
  • Biomedical Engineering
  • Applied Mathematics

Cite this

Honiden, S., Houle, M. E., Sommer, C., & Wolff, M. (2009). Approximate shortest path queries in graphs using Voronoi duals. In 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009 (pp. 53-62). [5362417] https://doi.org/10.1109/ISVD.2009.30

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

6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009. 2009. p. 53-62 5362417.

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

Honiden, S, Houle, ME, Sommer, C & Wolff, M 2009, Approximate shortest path queries in graphs using Voronoi duals. in 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009., 5362417, pp. 53-62, 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009, Copenhagen, Denmark, 09/6/23. https://doi.org/10.1109/ISVD.2009.30
Honiden S, Houle ME, Sommer C, Wolff M. Approximate shortest path queries in graphs using Voronoi duals. In 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009. 2009. p. 53-62. 5362417 https://doi.org/10.1109/ISVD.2009.30
Honiden, Shinichi ; Houle, Michael E. ; Sommer, Christian ; Wolff, Martin. / Approximate shortest path queries in graphs using Voronoi duals. 6th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2009. 2009. pp. 53-62
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