Affiliation:
1. Duke University, Durham, North Carolina
2. University of Illinois, Urbana-Champaign, Urbana, Illinois
3. University of Iowa, Iowa City, Iowa
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.
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Cited by
193 articles.
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