Nabil H. Mustafa

collaborators

3 papers

cs.LG2018

Optimal Bounds on the VC-dimension

Monika Csikos, Andrey Kupavskii, Nabil H. Mustafa

The VC-dimension of a set system is a way to capture its complexity and has been a key parameter studied extensively in machine learning and geometry communities. In this paper, we…

math.MG2018

Theorems of Carathéodory, Helly, and Tverberg without dimension

Karim Adiprasito, Imre Bárány, Nabil H. Mustafa +1

We prove a no-dimensional version of Carathédory's theorem: given an $n$ -element set $P \subset ℜ^{d}$ , a point $a \in \conv P$, and an integer $r \leq d$ , $r \leq n$ , there is a subse…

math.MG2018

Tverberg theorems over discrete sets of points

Jesús A. De Loera, Thomas A. Hogan, Frédéric Meunier +1

This paper discusses Tverberg-type theorems with coordinate constraints (i.e., versions of these theorems where all points lie within a subset $S \subset R^{d}$ and the inte…