A Practical Approach for Computing the Diameter of a Point Set

TL;DR

This paper introduces a simple, robust approximation algorithm for efficiently computing the diameter of point sets in high-dimensional space, adapting to input difficulty and performing well in practice.

Contribution

It presents a new diameter approximation algorithm that is sensitive to input complexity and offers fast, accurate results suitable for practical applications.

Findings

Algorithm is fast for most inputs

It adapts to the hardness of the problem

It demonstrates good empirical performance

Abstract

We present an approximation algorithm for computing the diameter of a point-set in $\Re^d$. The new algorithm is sensitive to the ``hardness'' of computing the diameter of the given input, and for most inputs it is able to compute the exact diameter extremely fast. The new algorithm is simple, robust, has good empirical performance, and can be implemented quickly. As such, it seems to be the algorithm of choice in practice for computing/approximating the diameter.