### Abstract

We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |

Editors | Anon |

Publisher | ACM |

Pages | 483-492 |

Number of pages | 10 |

State | Published - 1997 |

Event | Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA, USA Duration: Jan 5 1997 → Jan 7 1997 |

### Other

Other | Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | New Orleans, LA, USA |

Period | 1/5/97 → 1/7/97 |

### Fingerprint

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Discrete Mathematics and Combinatorics

### Cite this

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 483-492). ACM.

**Line transversals of balls and smallest enclosing cylinders in three dimensions.** / Agarwal, Pankaj K.; Aronov, Boris; Sharir, Micha.

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

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.*ACM, pp. 483-492, Proceedings of the 1996 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, USA, 1/5/97.

}

TY - GEN

T1 - Line transversals of balls and smallest enclosing cylinders in three dimensions

AU - Agarwal, Pankaj K.

AU - Aronov, Boris

AU - Sharir, Micha

PY - 1997

Y1 - 1997

N2 - We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

AB - We establish a near-cubic upper bound on the complexity of the space of line transversals of a collection of n balls in three dimensions; and show that the bound is almost tight, in the worst case. We apply this bound to obtain a near-cubic algorithm for computing a smallest infinite cylinder enclosing a given set of points or balls in 3-space. We also present an approximation algorithm for computing a smallest enclosing cylinder.

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UR - http://www.scopus.com/inward/citedby.url?scp=0030834867&partnerID=8YFLogxK

M3 - Conference contribution

SP - 483

EP - 492

BT - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

A2 - Anon, null

PB - ACM

ER -