### 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 R^{2}.

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 |

### Fingerprint

### 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

*Computing*,

*26*(4), 361-366. https://doi.org/10.1007/BF02237955

**A note on linear expected time algorithms for finding convex hulls.** / Devroye, L.; Toussaint, Godfried.

Research output: Contribution to journal › Article

*Computing*, vol. 26, no. 4, pp. 361-366. https://doi.org/10.1007/BF02237955

}

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

VL - 26

SP - 361

EP - 366

JO - Computing (Vienna/New York)

JF - Computing (Vienna/New York)

SN - 0010-485X

IS - 4

ER -