### Abstract

Let C^{+} and C^{−} be two collections of topological discs of arbitrary radii. The collection of discs is ‘topological’ in the sense that their boundaries are Jordan curves and each pair of Jordan curves intersect at most twice. We prove that the region ∪C^{+}−∪C^{−} has combinatorial complexity at most 10n-30 where p=|C^{+}|, q=|C^{−}| and n=p + q ≥ 5. Moreover, this bound is achievable. We also show bounds that are stated as functions of p and q. These are less precise.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings |

Publisher | Springer Verlag |

Pages | 577-588 |

Number of pages | 12 |

Volume | 709 LNCS |

ISBN (Print) | 9783540571551 |

State | Published - 1993 |

Event | 3rd Workshop on Algorithms and Data Structures, WADS 1993 - Montreal, Canada Duration: Aug 11 1993 → Aug 13 1993 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 709 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Workshop on Algorithms and Data Structures, WADS 1993 |
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Country | Canada |

City | Montreal |

Period | 8/11/93 → 8/13/93 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings*(Vol. 709 LNCS, pp. 577-588). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 709 LNCS). Springer Verlag.

**Combinatorial complexity of signed discs.** / Souvaine, Diane L.; Yap, Chee.

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

*Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings.*vol. 709 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 709 LNCS, Springer Verlag, pp. 577-588, 3rd Workshop on Algorithms and Data Structures, WADS 1993, Montreal, Canada, 8/11/93.

}

TY - GEN

T1 - Combinatorial complexity of signed discs

AU - Souvaine, Diane L.

AU - Yap, Chee

PY - 1993

Y1 - 1993

N2 - Let C+ and C− be two collections of topological discs of arbitrary radii. The collection of discs is ‘topological’ in the sense that their boundaries are Jordan curves and each pair of Jordan curves intersect at most twice. We prove that the region ∪C+−∪C− has combinatorial complexity at most 10n-30 where p=|C+|, q=|C−| and n=p + q ≥ 5. Moreover, this bound is achievable. We also show bounds that are stated as functions of p and q. These are less precise.

AB - Let C+ and C− be two collections of topological discs of arbitrary radii. The collection of discs is ‘topological’ in the sense that their boundaries are Jordan curves and each pair of Jordan curves intersect at most twice. We prove that the region ∪C+−∪C− has combinatorial complexity at most 10n-30 where p=|C+|, q=|C−| and n=p + q ≥ 5. Moreover, this bound is achievable. We also show bounds that are stated as functions of p and q. These are less precise.

UR - http://www.scopus.com/inward/record.url?scp=85029470840&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029470840&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540571551

VL - 709 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 577

EP - 588

BT - Algorithms and Data Structures - 3rd Workshop, WADS 1993, Proceedings

PB - Springer Verlag

ER -