### Abstract

Let S be a set of n points in R^{3}. Let ω* = ω*(S) be the width (i.e., thickness) of a minimum-width infinite cylindrical shell (the region between two co-axial cylinders) containing S. We first present an O(n^{5})-time algorithm for computing ω*, which as far as we know is the first nontrivial algorithm for this problem. We then present an O(n^{2+δ})-time algorithm, for any δ>0, that computes a cylindrical shell of width at most 26(1+1/n^{4/9})ω* containing S.

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

Publisher | SIAM |

Pages | 510-517 |

Number of pages | 8 |

State | Published - 2000 |

Event | 11th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA Duration: Jan 9 2000 → Jan 11 2000 |

### Other

Other | 11th Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | San Francisco, CA, USA |

Period | 1/9/00 → 1/11/00 |

### 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. 510-517). SIAM.

**Exact and approximation algorithms for minimum-width cylindrical shells.** / 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.*SIAM, pp. 510-517, 11th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, USA, 1/9/00.

}

TY - GEN

T1 - Exact and approximation algorithms for minimum-width cylindrical shells

AU - Agarwal, Pankaj K.

AU - Aronov, Boris

AU - Sharir, Micha

PY - 2000

Y1 - 2000

N2 - Let S be a set of n points in R3. Let ω* = ω*(S) be the width (i.e., thickness) of a minimum-width infinite cylindrical shell (the region between two co-axial cylinders) containing S. We first present an O(n5)-time algorithm for computing ω*, which as far as we know is the first nontrivial algorithm for this problem. We then present an O(n2+δ)-time algorithm, for any δ>0, that computes a cylindrical shell of width at most 26(1+1/n4/9)ω* containing S.

AB - Let S be a set of n points in R3. Let ω* = ω*(S) be the width (i.e., thickness) of a minimum-width infinite cylindrical shell (the region between two co-axial cylinders) containing S. We first present an O(n5)-time algorithm for computing ω*, which as far as we know is the first nontrivial algorithm for this problem. We then present an O(n2+δ)-time algorithm, for any δ>0, that computes a cylindrical shell of width at most 26(1+1/n4/9)ω* containing S.

UR - http://www.scopus.com/inward/record.url?scp=0033881364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033881364&partnerID=8YFLogxK

M3 - Conference contribution

SP - 510

EP - 517

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

PB - SIAM

ER -