Exact and Approximation Algorithms for Minimum-Width Cylindrical Shells (2001)
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BibTeX
@MISC{Agarwal01exactand,
author = {Pankaj K. Agarwal and Boris Aronov and Micha Sharir},
title = {Exact and Approximation Algorithms for Minimum-Width Cylindrical Shells},
year = {2001}
}
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Abstract
Let S be a set of n points in R 3 . Let ! = ! (S) be the width (i.e., thickness) of a minimum-width innite cylindrical shell (the region between two co-axial cylinders) containing S. We rst present an O(n 5 )-time algorithm for computing ! , which as far as we know is the rst nontrivial algorithm for this problem. We then present an O(n 2+ )-time algorithm, for any > 0, that computes a cylindrical shell of width at most 26(1 + 1=n 4=9 )! containing S. Work by P.A. was supported by Army Research Oce MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by NSF grants EIA{9870724, and CCR{9732787, by an NYI award, and by a grant from the U.S.-Israeli Binational Science Foundation. Work by B.A. was supported by a Sloan Research Fellowship and by a grant from the U.S.-Israeli Binational Science Foundation. Work by M.S. was supported by NSF Grants CCR-97-32101, CCR-94-24398, by grants from the U.S.-Israeli Binational Science Foundation, the G.I.F., the German-Isr...
