Algorithm for Finding an Exact Maximum Distance in E2 with Oexp(N) Complexity: Analysis and Experimental Results

TL;DR

This paper introduces a novel O(N) expected complexity algorithm for finding the maximum distance between two points in E2, significantly outperforming traditional methods in speed, especially on large datasets.

Contribution

The paper presents a new, simple, and robust algorithm with expected linear complexity for maximum distance calculation in E2, extendable to E3, with proven experimental efficiency.

Findings

Over 10,000 times faster than brute force for 10 million points

Over 4 times faster than convex hull diameter methods

Significant speed-up on large datasets

Abstract

This paper describes a novel and fast, simple and robust algorithm with O(N) expected complexity which enables to decrease run time needed to find the maximum distance of two points in E2. It can be easily modified for the E3 case in general. The proposed algorithm has been evaluated experimentally on larger different datasets in order to verify it and prove expected properties of it. Experiments proved the advantages of the proposed algorithm over the standard algorithms based on the Brute force, convex hull or convex hull diameters approaches. 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 Brute force algorithm for 10 mil. points randomly distributed points in E2 and over 4 times faster than convex hull diameter computation. The speed-up of the proposed algorithm grows with the number of points processed.