Abstract
Consider n independent identically distributed random vectors from Rd 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 | |
| State | Published - Dec 1 1981 |
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Keywords
- algorithms
- average complexity
- Convex hull
- geometrical complexity
ASJC Scopus subject areas
- Theoretical Computer Science
- Software
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics
Cite this
A note on linear expected time algorithms for finding convex hulls. / Devroye, L.; Toussaint, Godfried.
In: Computing, Vol. 26, No. 4, 01.12.1981, p. 361-366.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A note on linear expected time algorithms for finding convex hulls
AU - Devroye, L.
AU - Toussaint, Godfried
PY - 1981/12/1
Y1 - 1981/12/1
N2 - Consider n independent identically distributed random vectors from Rd 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.
AB - Consider n independent identically distributed random vectors from Rd 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.
KW - algorithms
KW - average complexity
KW - Convex hull
KW - geometrical complexity
UR - http://www.scopus.com/inward/record.url?scp=0019682117&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0019682117&partnerID=8YFLogxK
U2 - 10.1007/BF02237955
DO - 10.1007/BF02237955
M3 - Article
AN - SCOPUS:0019682117
VL - 26
SP - 361
EP - 366
JO - Computing (Vienna/New York)
JF - Computing (Vienna/New York)
SN - 0010-485X
IS - 4
ER -