### Abstract

We describe a powerful framework for designing efficient batch algorithms for certain large-scale dynamic problems that must be solved using external memory. The class of problems we consider, which we call colorable external-decomposable problems, include rectangle intersection, orthogonal line segment intersection, range searching, and point location. We are particularly interested in these problems in two and higher dimensions. They have numerous applications in geographic information systems (GIS), spatial databases, and VLSI and CAD design. We present simplified algorithms for problems previously solved by more complicated approaches (such as rectangle intersection), and we present efficient algorithms for problems not previously solved in an efficient way (such as point location and higher-dimensional versions of range searching and rectangle intersection). We give experimental results concerning the running time for our approach applied to the red-blue rectangle intersection problem, which is a key component of the extremely important database operation spatial join. Our algorithm scales well with the problem size, and for large problems sizes it greatly outperforms the well-known sweepline approach.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |

Editors | Anon |

Place of Publication | Philadelphia, PA, United States |

Publisher | SIAM |

Pages | 685-694 |

Number of pages | 10 |

State | Published - 1998 |

Event | Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA Duration: Jan 25 1998 → Jan 27 1998 |

### Other

Other | Proceedings of the 1998 9th Annual ACM SIAM Symposium on Discrete Algorithms |
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City | San Francisco, CA, USA |

Period | 1/25/98 → 1/27/98 |

### ASJC Scopus subject areas

- Chemical Health and Safety
- Software
- Safety, Risk, Reliability and Quality
- Discrete Mathematics and Combinatorics

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## Cite this

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*(pp. 685-694). SIAM.