Bibliographic Details
| Title: |
Approximating Extent Measures of Points. |
| Authors: |
Agarwal, Pankaj K.1 pankaj@cs.duke.edu, Har-Peled, Sariel2 sariel@uiuc.edu, Varadarajan, Kasturi R.3 kvaradar@cs.uiowa |
| Superior Title: |
Journal of the ACM. Jul2004, Vol. 51 Issue 4, p0-635. 30p. 6 Diagrams, 1 Chart. |
| Subject Terms: |
*APPROXIMATION theory, *FUNCTIONAL analysis, *ALGORITHMS, SPHERES |
| Abstract: |
We present a general technique for approximating various descriptors of the extent of a set P of n points in IR 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/εO(1) , with the property that (1-epsilon;)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. [ABSTRACT FROM AUTHOR] |
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| Database: |
Business Source Premier |