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On the convex hull of random points in a polytope

Published online by Cambridge University Press:  14 July 2016

Rex A. Dwyer
Rex A. Dwyer*
Affiliation:
Carnegie-Mellon University
*
∗Present address: Computer Science Department, North Carolina State University, Raleigh, NC 27695–8206, USA.
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Abstract

The convex hull of n points drawn independently from a uniform distribution on the interior of a d-dimensional polytope is investigated. It is shown that the expected number of vertices is O(logd–1n) for any polytope, the expected number of vertices is Ω(logd–1n) for any simple polytope, and the expected number of facets is O(logd–1n) for any simple polytope. An algorithm is presented for constructing the convex hull of such sets of points in linear average time.

Keywords

EXTREME POINTSGEOMETRIC PROBABILITYAVERAGE-CASE ANALYSIS OF ALGORITHMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 4 , December 1988 , pp. 688 - 699
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Supported by National Science Foundation Grant No. ECS-8418392.

This paper is dedicated to the memory of Professor Rebecca S. Nelson, esteemed teacher.

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