Theorem 1.2.3 For set P of n points in the plane, one can compute the closest pair of P in expected linear time.

2 Quadtrees - Hierarchical Grids

3 Well Separated Pairs Decomposition

The Well-Separated Pair Decomposition and Its Applications

3.1.1 The construction algorithm

4 Clustering - Definitions and Basic Algorithms

4.2 On $k$-center clustering

The $k$-center clustering is NP-Hard.

A simple 2-approximation algorithm

4.3 On $k$-median clustering

4.4 On $k$-means clustering

5 On Complexity, Sampling, and $epsilon$-Nets and $epsilon$-Samples