A simple approximation algorithm for the diameter of a set of points in an Euclidean plane.

Approximation algorithms with linear complexities are required in the treatments of big data, however, present algorithms cannot output the diameter of a set of points with arbitrary accuracy and near-linear complexity. By introducing the partition technique, we introduce a very simple approximation algorithm with arbitrary accuracy ε and a complexity of O(N + ε-1 log ε-1) for the cases that all points are located in an Euclidean plane. The error bounds are proved strictly, and are verified by numerical tests.