# Epsilon-approximations and epsilon-nets

## TL;DR

This paper discusses epsilon-approximations and epsilon-nets, which are methods using random samples to efficiently approximate properties of geometric configurations for combinatorial and algorithmic applications.

## Contribution

It introduces and analyzes the concepts of epsilon-approximations and epsilon-nets, highlighting their importance in geometric sampling and approximation.

## Key findings

- Epsilon-approximations effectively estimate geometric properties.
- Epsilon-nets provide small representative subsets for geometric configurations.
- The methods improve efficiency in geometric algorithms.

## 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.