### Abstract

We call a line l a separator for a set S of objects in the plane if l avoids all the objects and partitions S into two nonempty subsets, one consisting of objects lying above l and the other of objects lying below l. In this paper we present an O(n log n)-time algorithm for finding a separator line for a set of n segments, provided the ratio between the diameter of the set of segments and the length of the smallest segment is bounded. The general case is an 'n^{2}-hard' problem, in the sense defined in [10] (see also [8]). Our algorithm is based on the recent results of [15], concerning the union of 'fat' triangles, but we also include an analysis which improves the bounds obtained in [15].

Original language | English (US) |
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Pages (from-to) | 277-288 |

Number of pages | 12 |

Journal | Computational Geometry: Theory and Applications |

Volume | 3 |

Issue number | 5 |

DOIs | |

State | Published - Nov 1993 |

Externally published | Yes |

### ASJC Scopus subject areas

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

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## Cite this

*Computational Geometry: Theory and Applications*,

*3*(5), 277-288. https://doi.org/10.1016/0925-7721(93)90018-2