### Abstract

The many-faces problem for arrangements of circles in the plane was studied. The complexity of many faces and the algorithmic problem arised in a variety of problems including three-dimensional arrangements. The improved bounds on the complexity of m distinct faces in an arrangement of n circles were obtained. The bounds coincide with the best known bounds for the number of incidences between m points and n circles.

Original language | English (US) |
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Title of host publication | Annual Symposium on Foundations of Computer Science - Proceedings |

Pages | 74-83 |

Number of pages | 10 |

State | Published - 2001 |

Event | 42nd Annual Symposium on Foundations of Computer Science - Las Vegas, NV, United States Duration: Oct 14 2001 → Oct 17 2001 |

### Other

Other | 42nd Annual Symposium on Foundations of Computer Science |
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Country | United States |

City | Las Vegas, NV |

Period | 10/14/01 → 10/17/01 |

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundations of Computer Science - Proceedings*(pp. 74-83)

**On the complexity of many faces in arrangements of circles.** / Agarwal, P. K.; Aronov, B.; Sharir, M.

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

*Annual Symposium on Foundations of Computer Science - Proceedings.*pp. 74-83, 42nd Annual Symposium on Foundations of Computer Science, Las Vegas, NV, United States, 10/14/01.

}

TY - GEN

T1 - On the complexity of many faces in arrangements of circles

AU - Agarwal, P. K.

AU - Aronov, B.

AU - Sharir, M.

PY - 2001

Y1 - 2001

N2 - The many-faces problem for arrangements of circles in the plane was studied. The complexity of many faces and the algorithmic problem arised in a variety of problems including three-dimensional arrangements. The improved bounds on the complexity of m distinct faces in an arrangement of n circles were obtained. The bounds coincide with the best known bounds for the number of incidences between m points and n circles.

AB - The many-faces problem for arrangements of circles in the plane was studied. The complexity of many faces and the algorithmic problem arised in a variety of problems including three-dimensional arrangements. The improved bounds on the complexity of m distinct faces in an arrangement of n circles were obtained. The bounds coincide with the best known bounds for the number of incidences between m points and n circles.

UR - http://www.scopus.com/inward/record.url?scp=0035161812&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035161812&partnerID=8YFLogxK

M3 - Conference contribution

SP - 74

EP - 83

BT - Annual Symposium on Foundations of Computer Science - Proceedings

ER -