TY - JOUR

T1 - Diameter, width, closest line pair, and parametric searching

AU - Chazelle, Bernard

AU - Edelsbrunner, Herbert

AU - Guibas, Leonidas

AU - Sharir, Micha

PY - 1993/12

Y1 - 1993/12

N2 - 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(n 1+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(n 8/5+ε) algorithm for computing the closest pair in a set of n lines in space. All these algorithms are deterministic.

AB - 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(n 1+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(n 8/5+ε) algorithm for computing the closest pair in a set of n lines in space. All these algorithms are deterministic.

UR - http://www.scopus.com/inward/record.url?scp=51249169067&partnerID=8YFLogxK

U2 - 10.1007/BF02573973

DO - 10.1007/BF02573973

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AN - SCOPUS:51249169067

SN - 0179-5376

VL - 10

SP - 183

EP - 196

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

IS - 1

ER -