Splitting a Delaunay Triangulation in Linear Time |
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| Authors: | Chazelle Devillers Hurtado Mora Sacristan Teillaud |
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| Affiliation: | (1) Computer Science Department, Princeton University, 35 Olden Street, Princeton, NJ 08544, USA. chazelle@cs.princeton.edu. http://ftp.cs.princeton.edu/~chazelle/., US;(2) INRIA, BP93, 06902 Sophia-Antipolis, France. Olivier.Devillers@sophia.inria.fr, Monique.Teillaud@sophia.inria.fr. www-sop.inria.fr/prisme/., FR;(3) Departamento de Matemàtica Aplicada II, Universidad Politècnica de Catalunya, Pau Gargallo 5, 08028 Barcelona, Spain. hurtado@ma2.upc.es, mora@ma2.upc.es, vera@ma2.upc.es. www-ma2.upc.es/~geomc/., ES |
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| Abstract: | Abstract. Computing the Delaunay triangulation of n points requires usually a minimum of Ω(n log n) operations, but in some special cases where some additional knowledge is provided, faster algorithms can be designed. Given two sets of points, we prove that, if the Delaunay triangulation of all the points is known, the Delaunay triangulation of each set can be computed in randomized expected linear time. |
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| Keywords: | . Computational geometry Delaunay triangulation Voronoi diagrams Randomized algorithms. |
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