### Abstract

We show how any BSP tree T P for the endpoints of a set of n disjoint segments in the plane can be used to obtain a BSP tree of size O(n.depth(T P )) for the segments themselves, such that the range-searching efficiency remains almost the same. We apply this technique to obtain a BSP tree of size O(n log n) such that e-approximate range searching queries with any constant-complexity convex query range can be answered in O(min e>¿0{1/e¿+¿k e }log n) time, where k e is the number of segments intersecting the e-extended range. The same result can be obtained for disjoint constant-complexity curves, if we allow the BSP to use splitting curves along the given curves.
We also describe how to construct a linear-size BSP tree for low-density scenes consisting of n objects in R d such that e-approximate range searching with any constant-complexity convex query range can be done in O(logn+min ¿>0 {1/¿ (d-1) +k ¿ }) time.

Original language | English |
---|---|

Title of host publication | Foundations of Software Technology and Theoretical Computer Science (Proceedings 24th Conference, FSTTCS 2004, Chennai, India, December 16-18, 2004) |

Editors | K. Lodaya, M. Mahajan |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 110-121 |

ISBN (Print) | 3-540-24058-6 |

DOIs | |

Publication status | Published - 2004 |

### Publication series

Name | Lecture Notes in Computer Science |
---|---|

Volume | 3328 |

ISSN (Print) | 0302-9743 |

## Fingerprint Dive into the research topics of 'Approximate range searching using binary space partitions'. Together they form a unique fingerprint.

## Cite this

Berg, de, M., & Streppel, M. W. A. (2004). Approximate range searching using binary space partitions. In K. Lodaya, & M. Mahajan (Eds.),

*Foundations of Software Technology and Theoretical Computer Science (Proceedings 24th Conference, FSTTCS 2004, Chennai, India, December 16-18, 2004)*(pp. 110-121). (Lecture Notes in Computer Science; Vol. 3328). Springer. https://doi.org/10.1007/978-3-540-30538-5_10