### Abstract

The set P of n points in R^{d} in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | ACM |

Pages | 192-199 |

Number of pages | 8 |

State | Published - 1998 |

Event | Proceedings of the 1998 14th Annual Symposium on Computational Geometry - Minneapolis, MN, USA Duration: Jun 7 1998 → Jun 10 1998 |

### Other

Other | Proceedings of the 1998 14th Annual Symposium on Computational Geometry |
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City | Minneapolis, MN, USA |

Period | 6/7/98 → 6/10/98 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Geometry and Topology

### Cite this

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 192-199). ACM.

**Results on k-sets and j-facets via continuous motion.** / Andrzejak, Artur; Aronov, Boris; Har-Peled, Sariel; Seidel, Raimund; Welzl, Emo.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual Symposium on Computational Geometry.*ACM, pp. 192-199, Proceedings of the 1998 14th Annual Symposium on Computational Geometry, Minneapolis, MN, USA, 6/7/98.

}

TY - GEN

T1 - Results on k-sets and j-facets via continuous motion

AU - Andrzejak, Artur

AU - Aronov, Boris

AU - Har-Peled, Sariel

AU - Seidel, Raimund

AU - Welzl, Emo

PY - 1998

Y1 - 1998

N2 - The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

AB - The set P of n points in Rd in general position, where there are no i+1 points of a common (i-1)-flat and 1≤i≤d, is presented. A k-set of P is a set of S of k points in P that can be separated from P/S by a hyperplane. A j-facet is an oriented (d-1)-simplex spanned by d domains in P which has exactly j points from P on the positive side of its affine hull.

UR - http://www.scopus.com/inward/record.url?scp=0031639759&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031639759&partnerID=8YFLogxK

M3 - Conference contribution

SP - 192

EP - 199

BT - Proceedings of the Annual Symposium on Computational Geometry

PB - ACM

ER -