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 -