Fast Oexpected(N) Algorithm for Finding Exact Maximum Distance in E2 Instead of O(N2) or O(N lgN)

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 106 points randomly distributed points in E2. Experiments proved the advantages of the proposed algorithm over the standard algorithm and convex hull diameters approaches.