## Efficient 3-D Range Searching in External Memory (1995)

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Venue: | In Proc. ACM Symp. on Theory of Computation |

Citations: | 31 - 4 self |

### BibTeX

@INPROCEEDINGS{Vengroff95efficient3-d,

author = {Darren Erik Vengroff and Jeffrey Scott Vitter},

title = {Efficient 3-D Range Searching in External Memory},

booktitle = {In Proc. ACM Symp. on Theory of Computation},

year = {1995},

pages = {192--201}

}

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### Abstract

We present a new approach to designing data structures for the important problem of externalmemory range searching in two and three dimensions. We construct data structures for answering range queries in O((log log log B N) log B N + K=B) I/O operations, where N is the number of points in the data structure, B is the I/O block size, and K is the number of points in the answer to the query. Our data structures answer a longstanding open problem by providing three dimensional results comparable to those provided by [8, 10] for the two dimensional case, though completely new techniques are used. Ours is the first 3-D range search data structure that simultaneously achieves both a base-B logarithmic search overhead (namely, (log log log B N) log B N) and a fully blocked output component (namely, K=B). This gives us an overall I/O complexity extremely close to the well-known lower bound of \Omega\Gamma/89 B N +K=B). We base our data structures on the novel concept of B-approximate boundarie...

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Computer Graphics : Principles and Practice
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- 1990
(Show Context)
Citation Context ...at are contained in ae. Range searching is a fundamental primitive in several large-scale applications, including spatial databases and geographic information systems (GIS) [9, 6, 1, 11, 4], graphics =-=[3]-=-, indexing in objectoriented databases [5, 7], and constraint logic programming [7]. When the data are too large to fit in main memory and must reside on disk, the Input/Output (I/O) communication can... |

246 | Making data structures persistent
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- 1989
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Citation Context ...he projection of one of these corners into the x; y plane; thus the complexity of the decomposition is O(N ). The point location problem can be thus solved in O(log B N) I/Os with a persistent B-tree =-=[2]-=- that occupies O(N=B) blocks. Using techniques analogous to those of Section 2.2, we can build a set of layered approximate boundaries in three dimensions and to answer (1; 1; 1)-sided queries. Follow... |

173 |
Fvndarnentals of Spatial Information Systems
- Laurini, Thompson
- 1995
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Citation Context ...ts in the data structure that are contained in ae. Range searching is a fundamental primitive in several large-scale applications, including spatial databases and geographic information systems (GIS) =-=[9, 6, 1, 11, 4]-=-, graphics [3], indexing in objectoriented databases [5, 7], and constraint logic programming [7]. When the data are too large to fit in main memory and must reside on disk, the Input/Output (I/O) com... |

113 | Indexing for data models with constraints and classes
- KANELLAKIS, RAMASWAMY, et al.
- 1993
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Citation Context ... a fundamental primitive in several large-scale applications, including spatial databases and geographic information systems (GIS) [9, 6, 1, 11, 4], graphics [3], indexing in objectoriented databases =-=[5, 7]-=-, and constraint logic programming [7]. When the data are too large to fit in main memory and must reside on disk, the Input/Output (I/O) communication can become a very severe bottleneck. In d-dimens... |

79 |
The P-range tree: a new data structure for range searching in secondard memory
- Subramanian, Ramaswamy
- 1995
(Show Context)
Citation Context ...I/O block size, and K is the number of points in the answer to the query. Our data structures answer a longstanding open problem by providing three dimensional results comparable to those provided by =-=[8, 10]-=- for the two dimensional case, though completely new techniques are used. Ours is the first 3-D range search data structure that simultaneously achieves both a base-B logarithmic search overhead (name... |

52 | Path caching: A technique for optimal external searching
- RAMASWAMY, SUBRAMANIAN
- 1994
(Show Context)
Citation Context ...I/O block size, and K is the number of points in the answer to the query. Our data structures answer a longstanding open problem by providing three dimensional results comparable to those provided by =-=[8, 10]-=- for the two dimensional case, though completely new techniques are used. Ours is the first 3-D range search data structure that simultaneously achieves both a base-B logarithmic search overhead (name... |

22 | OODB indexing by class-division
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- 1995
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Citation Context ... a fundamental primitive in several large-scale applications, including spatial databases and geographic information systems (GIS) [9, 6, 1, 11, 4], graphics [3], indexing in objectoriented databases =-=[5, 7]-=-, and constraint logic programming [7]. When the data are too large to fit in main memory and must reside on disk, the Input/Output (I/O) communication can become a very severe bottleneck. In d-dimens... |

20 |
Exploiting extensible DBMS in integrated geographic information systems
- Haas, Cody
- 1991
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Citation Context ...ts in the data structure that are contained in ae. Range searching is a fundamental primitive in several large-scale applications, including spatial databases and geographic information systems (GIS) =-=[9, 6, 1, 11, 4]-=-, graphics [3], indexing in objectoriented databases [5, 7], and constraint logic programming [7]. When the data are too large to fit in main memory and must reside on disk, the Input/Output (I/O) com... |

19 |
An intellegent information fusion system for handling the archiving and querying of terabyte-sized spatial databases
- Cromp
- 1993
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Citation Context ...ts in the data structure that are contained in ae. Range searching is a fundamental primitive in several large-scale applications, including spatial databases and geographic information systems (GIS) =-=[9, 6, 1, 11, 4]-=-, graphics [3], indexing in objectoriented databases [5, 7], and constraint logic programming [7]. When the data are too large to fit in main memory and must reside on disk, the Input/Output (I/O) com... |

3 |
Kreveld. Geographic information systems
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- 1995
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Citation Context |