Delaunay Triangulations in Linear Time? (Part I)
Computational Geometry
2009-12-13 v3 Data Structures and Algorithms
Abstract
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.
Cite
@article{arxiv.0812.0387,
title = {Delaunay Triangulations in Linear Time? (Part I)},
author = {Kevin Buchin},
journal= {arXiv preprint arXiv:0812.0387},
year = {2009}
}
Comments
8 pages, no figures; added footnote about newer algorithm