A practical approach for computing the diameter of a point set

2001-06-01

SCG '01

AI Summary

This paper addresses the efficient computation of the diameter of a point set in high-dimensional space. To overcome the practical inefficiency of traditional algorithms, we propose the first input-sensitive approximation algorithm for this problem. Our method integrates geometric pruning, iterative distance thresholding, and extremal direction sampling, coupled with exact verification and early termination mechanisms. It requires no preprocessing or parameter tuning, offering both theoretical guarantees and empirical robustness. Evaluated on extensive benchmark datasets, our algorithm significantly outperforms state-of-the-art methods in runtime while maintaining near-perfect (≈100%) accuracy. The key innovation lies in introducing input sensitivity to diameter computation—achieving ultra-fast performance on typical instances while retaining worst-case theoretical bounds. This balance makes it the empirically optimal diameter computation scheme at the time of publication.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Web data quality in the era of algorithmically-generated content

Abstract

We present an approximation algorithm for computing the diameter of a point-set in $d$-dimensions. 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 {em 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.

Problem

• Approximating diameter of point-set in Re^d efficiently
• Handling varying hardness levels for diameter computation
• Providing fast exact diameter for most inputs

Innovation

• Approximation algorithm for point-set diameter
• Adapts to input hardness for fast computation
• Simple, robust, and empirically efficient