8 citations · 10 across the 6 of their papers we have counts for
14 papers · 1 filter
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…
The complexity of sharing a pizza
Patrick Schnider
Assume you have a 2-dimensional pizza with ingredients that you want to share with your friend. For this you are allowed to cut the pizza using several straight cuts, and then…
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…
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…
Efficiently stabbing convex polygons and variants of the Hadwiger-Debrunner -theorem
Justin Dallant, Patrick Schnider
Hadwiger and Debrunner showed that for families of convex sets in with the property that among any of them some have a common point, the whole family can be…
Arrangements of Approaching Pseudo-Lines
Stefan Felsner, Alexander Pilz, Patrick Schnider
We consider arrangements of pseudo-lines in the Euclidean plane where each pseudo-line is represented by a bi-infinite connected -monotone curve , $x \in \m…