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Quickest Paths, Straight Skeletons, and the City Voronoi Diagram
 

Summary: Quickest Paths, Straight Skeletons, and the City
Voronoi Diagram
Oswin Aichholzer #
Franz Aurenhammer
Institute for Theoretical Computer Science
Graz University of Technology
{oaich,auren}@igi.tu­graz.ac.at
Bel’en Palop +
Departamento de Ciencias de la Computaci’on
Universidad Alcal’a de Henares, Madrid, Spain
b.palop@uah.es
Abstract
The city Voronoi diagram is induced by quickest paths, in the L 1 plane speeded
up by an isothetic transportation network. We investigate the rich geometric and
algorithmic properties of city Voronoi diagrams, and report on their use in processing
quickest­path queries.
In doing so, we revisit the fact that not every Voronoi­type diagram has inter­
pretations in both the distance model and the wavefront model. Especially, straight
skeletons are a relevant example where an interpretation in the former model is lack­
ing. We clarify the relationship between these models, and further draw a connection

  

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz
Technische Universität Graz, Institute for Software Technology

 

Collections: Computer Technologies and Information Sciences