 
Summary: Exact and Approximation Algorithms for MinimumWidth Cylindrical Shells \Lambda
Pankaj K. Agarwal y Boris Aronov z Micha Sharir x
Abstract
Let S be a set of n points in R 3 . Let ! \Lambda = ! \Lambda (S) be the width
(i.e., thickness) of a minimumwidth infinite cylindrical shell
(the region between two coaxial cylinders) containing S.
We first present an O(n 5 )time algorithm for computing ! \Lambda ,
which as far as we know is the first nontrivial algorithm for
this problem. We then present an O(n 2+ffi )time algorithm,
for any ffi ? 0, that computes a cylindrical shell of width at
most 26(1 + 1=n 4=9 )! \Lambda containing S.
1 Introduction
Given a line ` in R 3 and two real numbers 0 Ÿ r Ÿ R,
the cylindrical shell \Sigma(`; r; R) is the closed region lying
between the two coaxial cylinders of radii r and R with
` as their axis, i.e.,
\Sigma(`; r; R) = fp 2 R 3 j r Ÿ d(p; `) Ÿ Rg;
where d(p; `) is the Euclidean distance between point p
and line `. The width of \Sigma(`; r; R) is R\Gammar. Let S be a set
of n points in R 3 . How well S fits a cylindrical surface
