Smallest enclosing cylinders
This paper addresses the complexity of computing the smallest-radius infinite cylinder that encloses an input set of n points in 3-space. We show that the problem can be solved in time O(n(4) log(O(1)) n) in an algebraic complexity model. We also achieve a time of O(n(4)L . mu(L)) in st bit complexity model where L is the maximum bit size of input numbers and mu(L) is the complexity of multiplying two L bit integers. These and several other results highlight a general linearization technique which transforms nonlinear problems into some higher-dimensional but linear problems. The; technique is reminiscent of the use of Plucker coordinates, and is used here in conjunction with Megiddo's parametric searching. We further report on experimental work comparing the practicality of an exact with that of a numerical strategy.
smallest enclosing cylinder parametric search geometric optimization epsilon-approximation algorithms best-fit line