### Abstract

The orthogonal segment intersection search problem is stated as follows: given a set S of n orthogonal segments in the plane, report all the segments of S that intersect a given orthogonal query segment. For this problem, we propose a simple and practical algorithm based on bucketing techniques. It constructs, in O(n) time preprocessing, a search structure of size O(n) so that all the segments of S intersecting a query segment can be reported in O(k) time in the average case, where k is the number of the reported segments. The proposed algorithm as well as existing algorithms is implemented in FORTRAN, and their practical efficiencies are investigated through computational experiments. It is shown that our O(k) search time, O(n) space, and O(n) preprocessing time algorithm is in practice the most efficient among the algorithms tested.

Original language | English |
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Pages (from-to) | 61-76 |

Number of pages | 16 |

Journal | Algorithmica |

Volume | 4 |

Issue number | 1-4 |

DOIs | |

Publication status | Published - 1989 Jun |

Externally published | Yes |

### Keywords

- Bucketing
- Filtering search
- Layered segment tree
- Practical efficiency
- Priority search tree
- Segment intersection search
- VLSI design

### ASJC Scopus subject areas

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

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## Cite this

*Algorithmica*,

*4*(1-4), 61-76. https://doi.org/10.1007/BF01553879