## Abstract

We develop a cache-oblivious data structure for storing a set S of N axis-aligned rectangles in the plane, such that all rectangles in 5 intersecting a query rectangle or point can be found efficiently. Our structure is an axis-aligned bounding-box hierarchy and as such it is the first cache-oblivious R-tree with provable performance guarantees. If no point in the plane is contained in B or more rectangles in S, the structure answers a rectangle query using O(√N/B+T/B) memory transfers and a point query using O((N/B) ^{e}) memory transfers for any ε > 0, where B is the block size of memory transfers between any two levels of a multilevel memory hierarchy. We also develop a variant of our structure that achieves the same performance on input sets with arbitrary overlap among the rectangles. The rectangle query bound matches the bound of the best known linear-space cache-aware structure.

Original language | English |
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Title of host publication | SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry, June 2005 |

Publisher | Association for Computing Machinery, Inc |

Pages | 170-179 |

Number of pages | 10 |

DOIs | |

Publication status | Published - 2005 |

Event | 21st Annual Symposium on Computational Geometry, SCG'05 - Pisa, Italy Duration: 6 Jun 2005 → 8 Jun 2005 |

### Conference

Conference | 21st Annual Symposium on Computational Geometry, SCG'05 |
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Country/Territory | Italy |

City | Pisa |

Period | 6/06/05 → 8/06/05 |

## Keywords

- Cache-oblivious data structures
- Geometric data structures
- I/O-efficiency
- R-trees