  $\newcommand{\floor}[1]{\left\lfloor {#1} \right\rfloor}
\renewcommand{\Re}{\mathbb{R}}$
  Tverberg's theorem states that a set of $n$ points in $\Re^d$ can be
partitioned into $\floor{n/(d+1)}$ sets with a common intersection. A point in
this intersection (aka Tverberg point) is a centerpoint of the input point set,
and the Tverberg partition provides a compact proof of this, which is
algorithmically useful.
  Unfortunately, computing a Tverberg point exactly requires $n^{O(d^2)}$ time.
We provide several new approximation algorithms for this problem, which improve
either the running time or quality of approximation, or both. In particular, we
provide the first strongly polynomial (in both $n$ and $d$) approximation
algorithm for finding a Tverberg point.

Computational Geometry