Diameter, width, closest line pair, and parametric searching

B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, Discrete & Computational Geometry 10 (1993) 183–196.

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Abstract
We apply Megiddo's parametric searching technique to several geometric optimization problems and derive significantly improved solutions for them. We obtain, for any fixed ε>0, an O(n1+ε) algorithm for computing the diameter of a point set in 3-space, an O(8/5+ε) algorithm for computing the width of such a set, and on O(n8/5+ε) algorithm for computing the closest pair in a set of n lines in space. All these algorithms are deterministic.
Publishing Year
Date Published
1993-12-01
Journal Title
Discrete & Computational Geometry
Volume
10
Issue
1
Page
183 - 196
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Chazelle B, Edelsbrunner H, Guibas L, Sharir M. Diameter, width, closest line pair, and parametric searching. Discrete & Computational Geometry. 1993;10(1):183-196. doi:10.1007/BF02573973
Chazelle, B., Edelsbrunner, H., Guibas, L., & Sharir, M. (1993). Diameter, width, closest line pair, and parametric searching. Discrete & Computational Geometry, 10(1), 183–196. https://doi.org/10.1007/BF02573973
Chazelle, Bernard, Herbert Edelsbrunner, Leonidas Guibas, and Micha Sharir. “Diameter, Width, Closest Line Pair, and Parametric Searching.” Discrete & Computational Geometry 10, no. 1 (1993): 183–96. https://doi.org/10.1007/BF02573973.
B. Chazelle, H. Edelsbrunner, L. Guibas, and M. Sharir, “Diameter, width, closest line pair, and parametric searching,” Discrete & Computational Geometry, vol. 10, no. 1, pp. 183–196, 1993.
Chazelle B, Edelsbrunner H, Guibas L, Sharir M. 1993. Diameter, width, closest line pair, and parametric searching. Discrete & Computational Geometry. 10(1), 183–196.
Chazelle, Bernard, et al. “Diameter, Width, Closest Line Pair, and Parametric Searching.” Discrete & Computational Geometry, vol. 10, no. 1, Springer, 1993, pp. 183–96, doi:10.1007/BF02573973.

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