Discrete & Computational Geometry

, Volume 31, Issue 1, pp 17–35 | Cite as

Quickest Paths, Straight Skeletons, and the City Voronoi Diagram

Article

Abstract

The city Voronoi diagram is induced by quickest paths in the L 1plane, made faster by an isothetic transportation network. We investigate the rich geometric and algorithmic properties of city Voronoi diagrams, and report on their use in processing quickest-path queries. In doing so, we revisit the fact that not every Voronoi-type diagram has interpretations in both the distance model and the wavefront model. Especially, straight skeletons are a relevant example where an interpretation in the former model is lacking. We clarify the relationship between these models, and further draw a connection to the bisector-defined abstract Voronoi diagram model, with the particular goal of computing the city Voronoi diagram efficiently.

Keywords

Voronoi Diagram Transportation Network Distance Model Diagram Model Algorithmic Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Institute for Theoretical Computer Science, Graz University of Technology, Inffeldgasse 16b, A-8010 GrazAustria
  2. 2.Departamento de Ciencias de la Computación, Universidad Alcalá de Henares, MadridSpain

Personalised recommendations