Epsilon-approximations and epsilon-nets

Abstract

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 two related notions---$\epsilon$-approximations and $\epsilon$-nets---that capture the most important quantitative properties that one would expect from a random sample with respect to an underlying geometric configuration.

Chapter 47 in Handbook on Discrete and Computational Geometry, 3rd edition. 27 pages