Elsevier

Computational Geometry

Volume 68, March 2018, Pages 134-145
Computational Geometry

Forest-like abstract Voronoi diagrams in linear time

This paper is dedicated to Ferran Hurtado
https://doi.org/10.1016/j.comgeo.2017.06.013Get rights and content
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Abstract

Abstract Voronoi diagrams are a general framework covering many types of concrete diagrams for different types of sites or distance measures. Generalizing a famous result by Aggarwal et al. [1] we prove the following. Suppose it is known that inside a closed domain D the Voronoi diagram V(S) is a tree, and for each subset SS, a forest with one face per site. If the order of Voronoi regions of V(S) along the boundary of D is given, then V(S) inside D can be constructed in linear time.

Keywords

Voronoi diagrams
General distance
Abstract Voronoi diagrams
Linear-time algorithms
Forest structures

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This work was partially supported by the European Science Foundation (ESF) in the EUROCORES collaborative research project EuroGIGA/VORONOI, and partially by DFG (Kl 655/19) as part of a D-A-CH project.