A Probabilistic Approach to Reducing Algebraic Complexity of Delaunay Triangulations

  • Jean-Daniel Boissonnat
  • Ramsay Dyer
  • Arijit Ghosh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)


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.


Simplicial Complex Delaunay Triangulation Full Cell Good Link Distance Comparison 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jean-Daniel Boissonnat
    • 1
  • Ramsay Dyer
    • 2
  • Arijit Ghosh
    • 3
  1. 1.INRIASophia AntipolisFrance
  2. 2.University of GroningenGroningenThe Netherlands
  3. 3.Max-Planck-Institut für InformatikSaarbrückenGermany

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