Fast O_{expected}(N) Algorithm for Finding Exact Maximum Distance in E^2 Instead of O(N^2) or O(N lg N)

Abstract

This paper describes novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run-time needed to find an exact maximum distance of two points in E2. The proposed algorithm has been evaluated experimentally on larger different datasets. The proposed algorithm gives a significant speed-up to applications, when medium and large data sets are processed. It is over 10 000 times faster than the standard algorithm for 10^6 points randomly distributed points in E2. Experiments proved the advantages of the proposed algorithm over the standard algorithm and convex hull diameters approaches.