# An improved bound for weak epsilon nets in the plane

### Wednesday, May 2nd, 2018, 16:10

### Schreiber 309

### An improved bound for weak epsilon nets in the plane

### Natan Rubin, Ben Gurion University

### Abstract:

We show that for any set $P$ of $n$ points in the plane and $\eps>0$ there exists a set of $o\left(\frac{1}{\eps^{1.7}}\right)$ points in the plane that pierce every convex set $K$ with $|K\cap P|\geq \eps |P|$. This is the first improvement of the 1992 upper bound $O\left(\frac{1}{\eps^2}\right)$ of Alon, Bárány, Füredi, and Kleitman.