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Vertex Removal in Two Dimensional Delaunay Triangulation: Asymptotic Complexity is Pointless

Olivier Devillers 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : The theoretical complexity of vertex removal in a Delaunay triangulation is often given in terms of the degree d of the removed point with usual results O(d), O(d log d), or O(d²). In fact the asymptotic complexity is of poor interest since d is usually quite small. In this paper we carefully design code for small degrees 3 ≤ d ≤ 7, it improves the global behavior of the removal for random points by a factor of 2.
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https://hal.inria.fr/inria-00433107
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Submitted on : Wednesday, November 18, 2009 - 11:01:00 AM
Last modification on : Wednesday, February 2, 2022 - 3:55:43 PM
Long-term archiving on: : Tuesday, October 16, 2012 - 2:21:17 PM

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Olivier Devillers. Vertex Removal in Two Dimensional Delaunay Triangulation: Asymptotic Complexity is Pointless. [Research Report] RR-7104, INRIA. 2009, pp.15. ⟨inria-00433107⟩

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