### Abstract

We consider stabbing regions for a set S of n line segments in the plane, that is, regions in the plane that contain exactly one endpoint of each segment of S. Concretely, we provide efficient algorithms for reporting all combinatorially different stabbing regions for S for regions that can be described as the intersection of axis-parallel halfplanes; these are halfplanes, strips, quadrants, 3-sided rectangles, and rectangles. The running times are O(n) (for the halfplane case), O(n log n) (for strips, quadrants, and 3-sided rectangles), and O(n^{2} log n) (for rectangles).

Original language | English |
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Title of host publication | Fundamentals of Computation Theory - 20th International Symposium, FCT 2015, Proceedings |

Editors | Igor Walukiewicz, Adrian Kosowski |

Publisher | Springer Verlag |

Pages | 53-64 |

Number of pages | 12 |

ISBN (Print) | 9783319221762 |

DOIs | |

Publication status | Published - 2015 |

Event | 20th International Symposium on Fundamentals of Computation Theory, FCT 2015 - Gdansk, Poland Duration: 2015 Aug 17 → 2015 Aug 19 |

### 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 | 9210 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 20th International Symposium on Fundamentals of Computation Theory, FCT 2015 |
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Country | Poland |

City | Gdansk |

Period | 15/8/17 → 15/8/19 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Claverol, M., Garijo, D., Korman, M., Seara, C., & Silveira, R. I. (2015). Stabbing segments with rectilinear objects. In I. Walukiewicz, & A. Kosowski (Eds.),

*Fundamentals of Computation Theory - 20th International Symposium, FCT 2015, Proceedings*(pp. 53-64). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9210). Springer Verlag. https://doi.org/10.1007/978-3-319-22177-9_5