A Probabilistic Approach to Reducing Algebraic Complexity of Delaunay Triangulations
Abstract
We propose algorithms to compute the Delaunay triangulation of a point set L using only (squared) distance comparisons (i.e., predicates of degree 2). Our approach is based on the witness complex, a weak form of the Delaunay complex introduced by Carlsson and de Silva. We give conditions that ensure that the witness complex and the Delaunay triangulation coincide and we introduce a new perturbation scheme to compute a perturbed set L′ close to L such that the Delaunay triangulation and the witness complex coincide. Our perturbation algorithm is a geometric application of the Moser-Tardos constructive proof of the Lovász local lemma.
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Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Format : Figure, Image
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
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