# Randomized incremental construction of Delaunay and Voronoi diagrams

@article{Guibas2005RandomizedIC,
title={Randomized incremental construction of Delaunay and Voronoi diagrams},
author={Leonidas J. Guibas and Donald Ervin Knuth and Micha Sharir},
journal={Algorithmica},
year={2005},
volume={7},
pages={381-413}
}
• Published 1 July 1990
• Computer Science
• Algorithmica
In this paper we give a new randomized incremental algorithm for the construction of planar Voronoi diagrams and Delaunay triangulations. The new algorithm is more “on-line” than earlier similar methods, takes expected timeO(nℝgn) and spaceO(n), and is eminently practical to implement. The analysis of the algorithm is also interesting in its own right and can serve as a model for many similar questions in both two and three dimensions. Finally we demonstrate how this approach for constructing…
372 Citations
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