Smallest enclosing cylinders

E. Schömer, J. Sellen, M. Teichmann, Chee Yap

Research output: Contribution to journalArticle

Abstract

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 4L · μ(L)) in a bit complexity model where L is the maximum bit size of input numbers and μ(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 Plücker 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.

Original languageEnglish (US)
Pages (from-to)170-186
Number of pages17
JournalAlgorithmica (New York)
Volume27
Issue number2
StatePublished - 2000

Fingerprint

Algebraic Complexity
Linearization Techniques
Model Complexity
Nonlinear Problem
High-dimensional
Radius
Transform
Linearization
Integer
Computing
Model
Strategy

Keywords

  • ε-approximation algorithms
  • Best-fit line
  • Geometric optimization
  • Parametric search
  • Smallest enclosing cylinder

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Safety, Risk, Reliability and Quality

Cite this

Schömer, E., Sellen, J., Teichmann, M., & Yap, C. (2000). Smallest enclosing cylinders. Algorithmica (New York), 27(2), 170-186.

Smallest enclosing cylinders. / Schömer, E.; Sellen, J.; Teichmann, M.; Yap, Chee.

In: Algorithmica (New York), Vol. 27, No. 2, 2000, p. 170-186.

Research output: Contribution to journalArticle

Schömer, E, Sellen, J, Teichmann, M & Yap, C 2000, 'Smallest enclosing cylinders', Algorithmica (New York), vol. 27, no. 2, pp. 170-186.
Schömer E, Sellen J, Teichmann M, Yap C. Smallest enclosing cylinders. Algorithmica (New York). 2000;27(2):170-186.
Schömer, E. ; Sellen, J. ; Teichmann, M. ; Yap, Chee. / Smallest enclosing cylinders. In: Algorithmica (New York). 2000 ; Vol. 27, No. 2. pp. 170-186.
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