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

TL;DR

This paper introduces a novel expected O(N) algorithm for efficiently finding the maximum distance between two points in the plane, significantly outperforming traditional methods especially on large datasets.

Contribution

The paper presents a new expected linear-time algorithm for maximum distance computation in E^2, improving speed over existing quadratic and near-linear algorithms.

Findings

Over 10,000 times faster than standard algorithms for 1 million points

Experimental validation on diverse datasets confirms efficiency gains

Outperforms convex hull diameter approaches in speed

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.