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Furthest Site Abstract Voronoi Diagrams

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Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Meiser,  Stefan
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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MPI-I-92-135.pdf
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Citation

Mehlhorn, K., Meiser, S., & Rasch, R.(1992). Furthest Site Abstract Voronoi Diagrams (MPI-I-92-135). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-B70A-5
Abstract
Abstract Voronoi diagrams were introduced by R. Klein as a
unifying approach to Voronoi diagrams. In this paper we study
furthest site abstract Voronoi diagrams and give a unified mathematical
and algorithmic treatment for them. In particular, we show that furthest
site abstract Voronoi diagrams are trees, have
linear size, and that, given a set of $n$ sites, the
furthest site abstract Voronoi diagram can be computed by a
randomized algorithm in expected time $O(n\log n)$.