Fast Algorithm for Finding Maximum Distance with Space Subdivision in E2

TL;DR

This paper introduces a fast, robust algorithm for finding the maximum distance between two points in a set in the plane, using space subdivision techniques to improve efficiency over standard methods.

Contribution

The paper presents a novel algorithm combining polar subdivision and uniform grid division to efficiently eliminate points and speed up maximum distance computation in 2D.

Findings

Significant speedup over standard algorithms

Effective elimination of points before distance calculation

Robust and easy-to-implement approach

Abstract

Finding an exact maximum distance of two points in the given set is a fundamental computational problem which is solved in many applications. This paper presents a fast, simple to implement and robust algorithm for finding this maximum distance of two points in E2. This algorithm is based on a polar subdivision followed by division of remaining points into uniform grid. The main idea of the algorithm is to eliminate as many input points as possible before finding the maximum distance. The proposed algorithm gives the significant speed up compared to the standard algorithm.