### Abstract

Let C^{+} and C^{-} be two collections of topological discs. 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 less precise bounds that are stated as functions of p and q.

Original language | English (US) |
---|---|

Pages (from-to) | 207-223 |

Number of pages | 17 |

Journal | Computational Geometry: Theory and Applications |

Volume | 5 |

Issue number | 4 |

DOIs | |

State | Published - 1995 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*5*(4), 207-223. https://doi.org/10.1016/0925-7721(94)00026-X

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

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 5, no. 4, pp. 207-223. https://doi.org/10.1016/0925-7721(94)00026-X

}

TY - JOUR

T1 - Combinatorial complexity of signed discs

AU - Souvaine, Diane L.

AU - Yap, Chee

PY - 1995

Y1 - 1995

N2 - Let C+ and C- be two collections of topological discs. 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 less precise bounds that are stated as functions of p and q.

AB - Let C+ and C- be two collections of topological discs. 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 less precise bounds that are stated as functions of p and q.

UR - http://www.scopus.com/inward/record.url?scp=58149321264&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149321264&partnerID=8YFLogxK

U2 - 10.1016/0925-7721(94)00026-X

DO - 10.1016/0925-7721(94)00026-X

M3 - Article

VL - 5

SP - 207

EP - 223

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 4

ER -