Efficiently Computing All Delaunay Triangles Occurring over All Contiguous Subsequences

Authors Stefan Funke, Felix Weitbrecht

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Stefan Funke
  • Universität Stuttgart, Germany
Felix Weitbrecht
  • Universität Stuttgart, Germany

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Stefan Funke and Felix Weitbrecht. Efficiently Computing All Delaunay Triangles Occurring over All Contiguous Subsequences. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Given an ordered sequence of points P = {p₁, p₂, … , p_n}, we are interested in computing T, the set of distinct triangles occurring over all Delaunay triangulations of contiguous subsequences within P. We present a deterministic algorithm for this purpose with near-optimal time complexity O(|T|log n). Additionally, we prove that for an arbitrary point set in random order, the expected number of Delaunay triangles occurring over all contiguous subsequences is Θ(nlog n).

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
  • Computational Geometry
  • Delaunay Triangulation
  • Randomized Analysis


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