### 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

Agarwal, P. K., Aronov, B., & Sharir, M. (2001). On the complexity of many faces in arrangements of circles. In

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