Exact and approximation algorithms for minimum-width cylindrical shells

Let S be a set of n points in R-3. Let omega* be the width (i.e., thickness ) of a minimum-width infinite cylindrical shell (the region between two co- axial cylinders) containing S. We first present an O(n(5))-time algorithm f or computing omega*, which as far as we know is the first nontrivial algori thm for this problem. We then present an O(n(2+delta))- time algorithm, for any delta > 0, that computes a cylindrical shell of width at most 56 omega * containing S.