5 citations · 14 across the 7 of their papers we have counts for
3 papers · 1 filter
Bounding the size of an almost-equidistant set in Euclidean space
Andrey Kupavskii, Nabil H. Mustafa, Konrad J. Swanepoel
A set of points in d-dimensional Euclidean space is almost equidistant if among any three points of the set, some two are at distance 1. We show that an almost-equidistant set in $…
The discrete yet ubiquitous theorems of Carathéodory, Helly, Sperner, Tucker, and Tverberg
Jesus A. De Loera, Xavier Goaoc, Frédéric Meunier +1
We discuss five discrete results: the lemmas of Sperner and Tucker from combinatorial topology and the theorems of Carathéodory, Helly, and Tverberg from combinatorial geometry. We…
Epsilon-approximations and epsilon-nets
Nabil H. Mustafa, Kasturi R. Varadarajan
The use of random samples to approximate properties of geometric configurations has been an influential idea for both combinatorial and algorithmic purposes. This chapter considers…