Best and random approximation of a convex body by a polytope

TL;DR

This paper reviews how convex bodies can be approximated by polytopes, comparing optimal and random methods, and finds that random approximation performs nearly as well as the best possible approach.

Contribution

It provides an overview linking best and random approximation methods for convex bodies, highlighting the effectiveness of random approaches.

Findings

Random approximation is nearly as effective as best approximation.

The paper clarifies the relationship between optimal and random polytope approximations.

Abstract

In this paper, we give an overview of some results concerning best and random approximation of convex bodies by polytopes. We explain how both are linked and see that random approximation is almost as good as best approximation.