Delaunay Triangulations in Linear Time? (Part I)

Details Delaunay Triangulations in Linear Time? (Part I) Delaunay Triangulations in Linear Time? (Part I)

2008-12-01

arxiv.org/abs/0812.0387v3

Computer Science

Computational Geometry

8 pages, no figures; added footnote about newer algorithm

Scientific paper

We present a new and simple randomized algorithm for constructing the Delaunay triangulation using nearest neighbor graphs for point location. Under suitable assumptions, it runs in linear expected time for points in the plane with polynomially bounded spread, i.e., if the ratio between the largest and smallest pointwise distance is polynomially bounded. This also holds for point sets with bounded spread in higher dimensions as long as the expected complexity of the Delaunay triangulation of a sample of the points is linear in the sample size.

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