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cs.CG2022
Well-Separation and Hyperplane Transversals in High Dimensions
Helena Bergold, Daniel Bertschinger, Nicolas Grelier +2
A family of point sets in dimensions is well-separated if the convex hulls of any two disjoint subfamilies can be separated by a hyperplane. Well-separation is a strong ass…
cs.CG2021
Tukey Depth Histograms
Daniel Bertschinger, Jonas Passweg, Patrick Schnider
The Tukey depth of a flat with respect to a point set is a concept that appears in many areas of discrete and computational geometry. In particular, the study of centerpoints, cent…
cs.CG2020
Weighted Epsilon-Nets
Daniel Bertschinger, Patrick Schnider
Motivated by recent work of Bukh and Nivasch on one-sided -approximants, we introduce the notion of \emph{weighted -nets}. It is a geometric notion of app…