### Abstract

We analyze the behavior of two line arrangement algorithms, a sweepline algorithm and an incremental algorithm, in approximate arithmetic. The algorithms have running times O(n^{2} log n) and O(n^{2}) respectively. We show that each of these algorithms can be implemented to have O(n∈) relative error. This means that each algorithm produces an arrangement realized by a set of pseudolines so that each pseudoline differs from the corresponding line relatively by at most O(n∈). We also show that there is a line arrangement algorithm with O(n^{2} log n) running time and O(∈) relative error.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | Association for Computing Machinery |

Pages | 334-341 |

Number of pages | 8 |

Volume | Part F129851 |

ISBN (Print) | 0897914260 |

DOIs | |

State | Published - Jun 1 1991 |

Externally published | Yes |

Event | 7th Annual Symposium on Computational Geometry, SCG 1991 - North Conway, United States Duration: Jun 10 1991 → Jun 12 1991 |

### Other

Other | 7th Annual Symposium on Computational Geometry, SCG 1991 |
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Country | United States |

City | North Conway |

Period | 6/10/91 → 6/12/91 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

Fortune, S., & Milenkovic, V. (1991). Numerical stability of algorithms for line arrangements. In

*Proceedings of the Annual Symposium on Computational Geometry*(Vol. Part F129851, pp. 334-341). Association for Computing Machinery. https://doi.org/10.1145/109648.109685