### Abstract

We present an extensive experimental study comparing the performance of four algorithms for the following orthogonal segment intersection problem: given a set of horizontal and vertical line segments in the plane, report all intersecting horizontal-vertical pairs. The problem has important applications in VLSI layout and graphics, which are large-scale in nature. The algorithms under evaluation are our implementations of distribution sweep and three variations of plane sweep. Distribution sweep is specifically designed for the situations in which the problem is too large to be solved in internal memory, and theoretically has optimal I/O cost. Plane sweep is a well-known and powerful technique in computational geometry, and is optimal for this particular problem in terms of internal computation. The three variations of plane sweep differ by the sorting methods (external versus internal sorting) used in the preprocessing phase and the dynamic data structures (B-tree versus 2-3-4-tree) used in the sweeping phase. We generate the test data by three programs that use a random number generator while producing some interesting properties that are predicted by our theoretical analysis. The sizes of the test data range from 250 thousand segments to 2.5 million segments. The experiments provide detailed quantitative evaluation of the performance of the four algorithms, and the observed behavior of the algorithms is consistent with their theoretical properties. This is, to the best of our knowledge, the first experimental algorithmic study comparing the practical performance between external-memory algorithms and conventional algorithms with large-scale test data.

Original language | English (US) |
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Pages (from-to) | 211-236 |

Number of pages | 26 |

Journal | Computational Geometry: Theory and Applications |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Mar 1998 |

### Keywords

- B-tree
- Distribution sweep
- Experimentation
- External-memory algorithm
- Implementation
- Plane sweep
- Probabilistic analysis
- Segment intersection

### ASJC Scopus subject areas

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