Computing a Minimum-Width Cubic and Hypercubic Shell

04/15/2019

∙

by   Sang Won Bae, et al.

∙

0

∙

share

In this paper, we study the problem of computing a minimum-width axis-aligned cubic shell that encloses a given set of n points in a three-dimensional space. A cubic shell is a closed volume between two concentric and face-parallel cubes. Prior to this work, there was no known algorithm for this problem in the literature. We present the first nontrivial algorithm whose running time is O(n log^2 n). Our approach easily extends to higher dimension, resulting in an O(n^ d/2 log^d-1 n)-time algorithm for the hypercubic shell problem in d≥ 3 dimension.