### Abstract

Efficient dynamic algorithms are presented for four geometric intersection problems. These include: (1) reporting the subset of a set S of nonintersecting segments in the plane that are intersected by a query segment of fixed slope; (2) reporting the segments of S that are intersected by a query segment whose supporting line passes through a fixed point; (3) the orthogonal segment intersection search problem; and (4) the point enclosure problem for isothetic hyper-rectangles in d-dimensional space, d ≥ 2. These algorithms are the first linear-space solutions to Problems 1-3 and for Problem 4 in the plane. For Problem 3, the update time improves upon the previous best algorithm by a logarithmic factor without affecting the query time. For Problem 4, the update time either matches or improves upon the previous best algorithms, but the query time is larger by a logarithmic factor. No dynamic algorithms were known previously for Problems 1 and 2.

Original language | English (US) |
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Pages (from-to) | 251-258 |

Number of pages | 8 |

Journal | Information Processing Letters |

Volume | 36 |

Issue number | 5 |

DOIs | |

State | Published - Dec 1 1990 |

### Keywords

- Analysis of algorithms
- computational complexity
- computational geometry
- data structures
- design of algorithms

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## Cite this

*Information Processing Letters*,

*36*(5), 251-258. https://doi.org/10.1016/0020-0190(90)90151-M