Approximate shortest path queries in graphs using Voronoi duals

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose an approximation method to answer shortest path queries in graphs, based on hierarchical random sampling and Voronoi duals. The lowest level of the hierarchy stores the initial graph. At each higher level, we compute a simplification of the graph on the level below, by selecting a constant fraction of nodes. Edges are generated as the Voronoi dual within the lower level, using the selected nodes as Voronoi sites. This hierarchy allows for fast computation of approximate shortest paths for general graphs. The time-quality tradeoff decision can be made at query time. We provide bounds on the approximation ratio of the path lengths.

Original languageEnglish
JournalNII Technical Reports
Issue number7
Publication statusPublished - 2008 Aug 25
Externally publishedYes


  • Approximation
  • Graph algorithms
  • Shortest path
  • Voronoi

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications


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