### Abstract

For any set X of points (in any dimension) and any k equals 1, 2,. . . , we introduce the concept of the k-hull of X. The k-hull is the set of points p such that for any hyperplane containing p there are at least k points of X in each closed half-space determined by the hyperplane. Several computational problems related to k-hulls are studied here, including computing the k-hull and finding a point in the k-hull. Some of our algorithms are of interest in themselves because of the techniques employed; in particular, a 'parametric' searching technique is used in a nontrivial way.

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

Pages (from-to) | 61-77 |

Number of pages | 17 |

Journal | SIAM Journal on Computing |

Volume | 16 |

Issue number | 1 |

State | Published - Feb 1987 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Theoretical Computer Science

### Cite this

*SIAM Journal on Computing*,

*16*(1), 61-77.

**ON k-HULLS AND RELATED PROBLEMS.** / Cole, Richard; Sharir, Micha; Yap, Chee.

Research output: Contribution to journal › Article

*SIAM Journal on Computing*, vol. 16, no. 1, pp. 61-77.

}

TY - JOUR

T1 - ON k-HULLS AND RELATED PROBLEMS.

AU - Cole, Richard

AU - Sharir, Micha

AU - Yap, Chee

PY - 1987/2

Y1 - 1987/2

N2 - For any set X of points (in any dimension) and any k equals 1, 2,. . . , we introduce the concept of the k-hull of X. The k-hull is the set of points p such that for any hyperplane containing p there are at least k points of X in each closed half-space determined by the hyperplane. Several computational problems related to k-hulls are studied here, including computing the k-hull and finding a point in the k-hull. Some of our algorithms are of interest in themselves because of the techniques employed; in particular, a 'parametric' searching technique is used in a nontrivial way.

AB - For any set X of points (in any dimension) and any k equals 1, 2,. . . , we introduce the concept of the k-hull of X. The k-hull is the set of points p such that for any hyperplane containing p there are at least k points of X in each closed half-space determined by the hyperplane. Several computational problems related to k-hulls are studied here, including computing the k-hull and finding a point in the k-hull. Some of our algorithms are of interest in themselves because of the techniques employed; in particular, a 'parametric' searching technique is used in a nontrivial way.

UR - http://www.scopus.com/inward/record.url?scp=0023288651&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0023288651&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 61

EP - 77

JO - SIAM Journal on Computing

JF - SIAM Journal on Computing

SN - 0097-5397

IS - 1

ER -