Abstract
This paper addresses the problem of computing a minimum-width axis-aligned cubic shell enclosing a given set of n points in R3. 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(nlog2n) in the worst case. Our approach extends to higher dimension d>3, resulting in an algorithm in O(n⌊d∕2⌋logd−1n) expected time.
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