article

Approximating extent measures of points

Authors:

Pankaj K. Agarwal,

Sariel Har-Peled,

Kasturi R. VaradarajanAuthors Info & Claims

Journal of the ACM (JACM), Volume 51, Issue 4

Pages 606 - 635

https://doi.org/10.1145/1008731.1008736

Published: 01 July 2004 Publication History

Abstract

We present a general technique for approximating various descriptors of the extent of a set P of n points in R^d when the dimension d is an arbitrary fixed constant. For a given extent measure μ and a parameter ε > 0, it computes in time O(n + 1/ε^O(1)) a subset Q ⊆ P of size 1/ε^O(1), with the property that (1 − ε)μ(P) ≤ μ(Q) ≤ μ(P). The specific applications of our technique include ε-approximation algorithms for (i) computing diameter, width, and smallest bounding box, ball, and cylinder of P, (ii) maintaining all the previous measures for a set of moving points, and (iii) fitting spheres and cylinders through a point set P. Our algorithms are considerably simpler, and faster in many cases, than previously known algorithms.

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Approximating extent measures of points

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Published In

cover image Journal of the ACM

Journal of the ACM Volume 51, Issue 4

July 2004

181 pages

ISSN:0004-5411

EISSN:1557-735X

DOI:10.1145/1008731

Issue’s Table of Contents

Copyright © 2004 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 2004

Published in JACM Volume 51, Issue 4

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