On levels in arrangements and voronoi diagrams

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1991 Germany English Publisher:Springer Science and Business Media LLCJournal:Discrete & Computational Geometry, volume 6, pages 307-338 (issn: 0179-5376, eissn: 1432-0444,

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Authors: Mulmuley, K.;

doi: 10.1007/bf02574692

On levels in arrangements and voronoi diagrams

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Abstract

The author introduces a powerful technique of so-called \(\theta\) series and probabilistic games which are suitable for the analysis of combinatorial and algorithmical complexity of randomized geometric algorithms. Fundamental results concerning the construction of levels in an arrangement of hyperplanes and higher-order Voronoi diagrams in any dimension are obtained. I enjoyed the underlying mathematical analysis.

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Germany

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Keywords

510.mathematics, Voronoi diagrams, Analysis of algorithms and problem complexity, Computer graphics; computational geometry (digital and algorithmic aspects), arrangement of hyperplanes, Article

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