Smoothed complexity of convex hulls by witnesses and collectors

Olivier Devillers 1 Marc Glisse 2 Xavier Goaoc 3 Rémy Thomasse 2
1 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
2 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We present a simple technique for analyzing the size of geometric hypergraphs defined by random point sets. As an application we obtain upper and lower bounds on the smoothed number of faces of the convex hull under Euclidean and Gaussian noise and related results.
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Olivier Devillers, Marc Glisse, Xavier Goaoc, Rémy Thomasse. Smoothed complexity of convex hulls by witnesses and collectors. [Research Report] 8787, INRIA. 2015, pp.41. ⟨hal-01214021v2⟩

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