A note on linear expected time algorithms for finding convex hulls

L. Devroye; G. T. Toussaint

doi:10.1007/BF02237955

A note on linear expected time algorithms for finding convex hulls

L. Devroye, G. T. Toussaint

Computer Science

Research output: Contribution to journal › Article

Abstract

Consider n independent identically distributed random vectors from R^d with common density f, and let E (C) be the average complexity of an algorithm that finds the convex hull of these points. Most well-known algorithms satisfy E (C)=0(n) for certain classes of densities. In this note, we show that E (C)=0(n) for algorithms that use a "throw-away" pre-processing step when f is bounded away from 0 and ∞ on any nondegenerate rectangle of R².

Original language	English (US)
Pages (from-to)	361-366
Number of pages	6
Journal	Computing
Volume	26
Issue number	4
DOIs	https://doi.org/10.1007/BF02237955
State	Published - Dec 1 1981

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Keywords

Convex hull
algorithms
average complexity
geometrical complexity

ASJC Scopus subject areas

Software
Theoretical Computer Science
Numerical Analysis
Computer Science Applications
Computational Theory and Mathematics
Computational Mathematics

Cite this

Devroye, L., & Toussaint, G. T. (1981). A note on linear expected time algorithms for finding convex hulls. Computing, 26(4), 361-366. https://doi.org/10.1007/BF02237955

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10.1007/BF02237955