### Abstract

Kirkpatrick and Seidel [13,14] recently proposed an algorithm for computing the convex hull of n points in the plane that runs in O(n log h) worst case time, where h denotes the number of points on the convex hull of the set. Here a modification of their algorithm is proposed that is believed to run in O(n) expected time for many reasonable distributions of points. The above O(n log h) algorithmsare experimentally compared to the O(n log n) 'throw-away' algorithms of Akl, Devroye and Toussaint [2, 8, 20]. The results suggest that although the O(n Log h) algorithms may be the 'ultimate' ones in theory, they are of little practical value from the point of view of running time.

Original language | English (US) |
---|---|

Pages (from-to) | 29-34 |

Number of pages | 6 |

Journal | Pattern Recognition Letters |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1985 |

### Keywords

- algorithms
- complexity
- computational geometry
- Convex hull

### ASJC Scopus subject areas

- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Artificial Intelligence

### Cite this

*Pattern Recognition Letters*,

*3*(1), 29-34. https://doi.org/10.1016/0167-8655(85)90039-X

**On the ultimate convex hull algorithm in practice.** / McQueen, Mary M.; Toussaint, Godfried.

Research output: Contribution to journal › Article

*Pattern Recognition Letters*, vol. 3, no. 1, pp. 29-34. https://doi.org/10.1016/0167-8655(85)90039-X

}

TY - JOUR

T1 - On the ultimate convex hull algorithm in practice

AU - McQueen, Mary M.

AU - Toussaint, Godfried

PY - 1985/1/1

Y1 - 1985/1/1

N2 - Kirkpatrick and Seidel [13,14] recently proposed an algorithm for computing the convex hull of n points in the plane that runs in O(n log h) worst case time, where h denotes the number of points on the convex hull of the set. Here a modification of their algorithm is proposed that is believed to run in O(n) expected time for many reasonable distributions of points. The above O(n log h) algorithmsare experimentally compared to the O(n log n) 'throw-away' algorithms of Akl, Devroye and Toussaint [2, 8, 20]. The results suggest that although the O(n Log h) algorithms may be the 'ultimate' ones in theory, they are of little practical value from the point of view of running time.

AB - Kirkpatrick and Seidel [13,14] recently proposed an algorithm for computing the convex hull of n points in the plane that runs in O(n log h) worst case time, where h denotes the number of points on the convex hull of the set. Here a modification of their algorithm is proposed that is believed to run in O(n) expected time for many reasonable distributions of points. The above O(n log h) algorithmsare experimentally compared to the O(n log n) 'throw-away' algorithms of Akl, Devroye and Toussaint [2, 8, 20]. The results suggest that although the O(n Log h) algorithms may be the 'ultimate' ones in theory, they are of little practical value from the point of view of running time.

KW - algorithms

KW - complexity

KW - computational geometry

KW - Convex hull

UR - http://www.scopus.com/inward/record.url?scp=0039807328&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039807328&partnerID=8YFLogxK

U2 - 10.1016/0167-8655(85)90039-X

DO - 10.1016/0167-8655(85)90039-X

M3 - Article

AN - SCOPUS:0039807328

VL - 3

SP - 29

EP - 34

JO - Pattern Recognition Letters

JF - Pattern Recognition Letters

SN - 0167-8655

IS - 1

ER -