Bernal, J.
(1990),
On the expected complexity of the 3-dimensional Voronoi diagram, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.IR.4321
(Accessed October 10, 2025)
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On the expected complexity of the 3-dimensional Voronoi diagram
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Abstract
Let 5 be a set of n sites chosen independently from a uniform distribution in a cube in 3dimensional Euclidean space. In this paper, work by Bentley, Weide and Yao is extended to show that the Voronoi diagram for 5 has an expected 0{n) number of faces. A consequence of the proof of this result is that the Voronoi diagram for 5 can be constructed in expected 0[n) time.Citation
NIST Interagency/Internal Report (NISTIR) - 4321
Report Number
4321
NIST Pub Series
Pub Type
NIST Pubs
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Keywords
algorithm, computational geometry, expected complexity, expected linear, expected time analysis, Voronoi diagram
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Created May 1, 1990, Updated November 10, 2018