### Abstract

Let Γ be a collection of unbounded x-monotone Jordan arcs intersecting at most twice each other, which we call pseudo-parabolas, since two axis parallel parabolas intersects at most twice. We investigate how to cut pseudo-parabolas into the minimum number of curve segments so that each pair of segments intersect at most once. We give an Ω(n^{4/3}) lower bound and O(n^{5/3}) upper bound. We give the same bounds for an arrangement of circles. Applying the upper bound, we give an O(n^{23/12}) bound on the complexity of a level of pseudo-parabolas, and O(n^{11/6}) bound on the complexity of a combinatorially concave chain of pseudo parabolas. We also give some upperbounds on the number of transitions of the minimum weight matroid base when the weight of each element changes as a quadratic function of a single parameter.

Original language | English |
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Title of host publication | Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995 |

Publisher | Association for Computing Machinery |

Pages | 230-237 |

Number of pages | 8 |

ISBN (Electronic) | 0897917243 |

DOIs | |

Publication status | Published - 1995 Sep 1 |

Event | 11th Annual Symposium on Computational Geometry, SCG 1995 - Vancouver, Canada Duration: 1995 Jun 5 → 1995 Jun 7 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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Volume | Part F129372 |

### Other

Other | 11th Annual Symposium on Computational Geometry, SCG 1995 |
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Country | Canada |

City | Vancouver |

Period | 95/6/5 → 95/6/7 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

*Proceedings of the 11th Annual Symposium on Computational Geometry, SCG 1995*(pp. 230-237). (Proceedings of the Annual Symposium on Computational Geometry; Vol. Part F129372). Association for Computing Machinery. https://doi.org/10.1145/220279.220304