Splitting a delaunay triangulation in linear time

B. Chazelle; O. Devillers; F. Hurtado; M. Mora; V. Sacristán; M. Teillaud

doi:10.1007/s00453-002-0939-8

Splitting a delaunay triangulation in linear time

B. Chazelle, O. Devillers, F. Hurtado, M. Mora, V. Sacristán, M. Teillaud

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

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.

Original language	English (US)
Pages (from-to)	39-46
Number of pages	8
Journal	Algorithmica (New York)
Volume	34
Issue number	1
DOIs	https://doi.org/10.1007/s00453-002-0939-8
State	Published - 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Computer Science
Computer Science Applications
Applied Mathematics

Keywords

Computational geometry
Delaunay triangulation
Randomized algorithms
Voronoi diagrams

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10.1007/s00453-002-0939-8

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AU - Chazelle, B.

AU - Devillers, O.

AU - Hurtado, F.

AU - Mora, M.

AU - Sacristán, V.

AU - Teillaud, M.

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

KW - Computational geometry

KW - Delaunay triangulation

KW - Randomized algorithms

KW - Voronoi diagrams

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Splitting a delaunay triangulation in linear time

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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