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A Probabilistic Approach to Reducing Algebraic Complexity of Delaunay Triangulations

Jean-Daniel Boissonnat 1 Ramsay Dyer 2 Arijit Ghosh 3
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
3 Algorithms and Complexity
MPII - Max-Planck-Institut für Informatik
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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Submitted on : Wednesday, October 7, 2015 - 5:05:39 PM
Last modification on : Friday, April 30, 2021 - 9:55:53 AM
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Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh. A Probabilistic Approach to Reducing Algebraic Complexity of Delaunay Triangulations. Algorithms - ESA 2015, Sep 2015, Patras, Greece. pp.595-606, ⟨10.1007/978-3-662-48350-3_50⟩. ⟨hal-01213070⟩



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