## On Packing R-trees (1993)

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Venue: | In ACM CIKM |

Citations: | 240 - 16 self |

### BibTeX

@INPROCEEDINGS{Faloutsos93onpacking,

author = {C. Faloutsos and Copyright C. Faloutsos},

title = {On Packing R-trees},

booktitle = {In ACM CIKM},

year = {1993}

}

### Years of Citing Articles

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### Abstract

– main idea; file structure – algorithms: insertion/split – deletion – search: range, nn, spatial joins – performance analysis – variations (packed; hilbert;...) 15-721 Copyright: C. Faloutsos (2001) 2 Problem • Given a collection of geometric objects (points, lines, polygons,...) • organize them on disk, to answer spatial queries (range, nn, etc) 15-721 Copyright: C. Faloutsos (2001) 3 1 (Who cares?)

### Citations

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Citation Context ...is the point query or stabbing query, where the query rectangle degenerates to a point. We focus on R-trees, which is one of the most efficient methods that support range queries. The original R-tree =-=[13]-=- and almost all of its variants are designed for a dynamic environment, being able to handle insertions and deletions. Operating in this mode, the R-tree guarantees that the space utilization is at le... |

1272 | The design and analysis of spatial data structures - Samet - 1989 |

1265 |
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Citation Context ...ionality space [15]; methods that use linear quadtrees [8] [1] or, equivalently, the zordering [21] or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees =-=[4]-=-, k-d-B-trees [23], hB-trees [19], cell-trees [11] e.t.c.) One of the most promising approaches in the last class is the R-tree [13]. It is the extension of the B-tree for multidimensional objects. A ... |

1102 | B.: ‘The R*-tree: An Efficient and Robust Access Method for Points and Rectangles
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Citation Context ...s are designed for a dynamic environment, being able to handle insertions and deletions. Operating in this mode, the R-tree guarantees that the space utilization is at least 50%; experimental results =-=[3] sho-=-wed that the average utilization is �� 70%. However, for a static set of data rectangles, we should be able to do better. Improving the space utilization through careful packing will have a two be... |

904 |
Computer Vision
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Citation Context ...Ss) of the near future is the ability to handle spatial data. Spatial data arise in many applications, including: Cartography [27]; Computer-Aided Design (CAD) [22] [12]; computer vision and robotics =-=[2]-=-; traditional databases, where a record with k attributes corresponds to a point in a k-d space; temporal databases, where time can be considered as one more dimension [18]; scientific databases, with... |

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Citation Context ...5]; methods that use linear quadtrees [8] [1] or, equivalently, the zordering [21] or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees =-=[23]-=-, hB-trees [19], cell-trees [11] e.t.c.) One of the most promising approaches in the last class is the R-tree [13]. It is the extension of the B-tree for multidimensional objects. A geometric object i... |

307 | e R + -Tree: A Dynamic Index for Multi-Dimensional Objects
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Citation Context ... structure for the R-tree of the previous figure (fanout=3) the best trade-off between splitting time and search performance. Subsequent work on R-trees includes the work by Greene [9], the R + -tree =-=[26]-=-, R-trees using Minimum Bounding Polygons [16], and finally, the R -tree [3], which seems to have the best performance among the R-tree variants. The main idea in the R -tree is the concept of forced ... |

254 |
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Citation Context ...cked R-tree' algorithm 0 1 2 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 H H H 1 2 3 Figure 5: Hilbert Curves of order 1, 2 and 3 infinity, the resulting curve is a fractal, with a fractal dimension of 2 =-=[20]-=-. The Hilbert curve can be generalized for higher dimensionalities. Algorithms to draw the two-dimensional curve of a given order, can be found in [10], [17]. An algorithm for higher dimensionalities ... |

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Citation Context ...: methods that transform rectangles into points in a higher dimensionality space [15]; methods that use linear quadtrees [8] [1] or, equivalently, the zordering [21] or other space filling curves [7] =-=[17]-=-; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [23], hB-trees [19], cell-trees [11] e.t.c.) One of the most promising approaches in the last class is the R-tree [13]. I... |

197 | The hb-tree: a multi-attribute indexing method with good guaranteed performance
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Citation Context ...t use linear quadtrees [8] [1] or, equivalently, the zordering [21] or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [23], hB-trees =-=[19]-=-, cell-trees [11] e.t.c.) One of the most promising approaches in the last class is the R-tree [13]. It is the extension of the B-tree for multidimensional objects. A geometric object is represented b... |

182 |
Spatial Query Processing in an Object-Oriented Database System
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Citation Context ...ods fall in the following broad classes: methods that transform rectangles into points in a higher dimensionality space [15]; methods that use linear quadtrees [8] [1] or, equivalently, the zordering =-=[21]-=- or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [23], hB-trees [19], cell-trees [11] e.t.c.) One of the most promising approaches ... |

157 | S.: ‘Fractals for Secondary Key Retrieval
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Citation Context ...sses: methods that transform rectangles into points in a higher dimensionality space [15]; methods that use linear quadtrees [8] [1] or, equivalently, the zordering [21] or other space filling curves =-=[7]-=- [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [23], hB-trees [19], cell-trees [11] e.t.c.) One of the most promising approaches in the last class is the R-tree [1... |

156 | LEIFKER D.: Direct spatial search on pictorial databases using packed R-trees
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Citation Context ...e winning variation (`2D-c') was the one that sorts the rectangles according to the hilbert value of the center. This variation consistently outperforms the packing method of Roussopoulos and Leifker =-=[24]-=-, as well as other R-tree variants. The performance gain of the our method seems to increase with the skeweness of the data distribution; specifically, on the (highly skewed) TIGER dataset, it achieve... |

149 |
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Citation Context ... survey can be found in [25]. These methods fall in the following broad classes: methods that transform rectangles into points in a higher dimensionality space [15]; methods that use linear quadtrees =-=[8]-=- [1] or, equivalently, the zordering [21] or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [23], hB-trees [19], cell-trees [11] e.t.... |

88 |
Extensible query processing in Starburst
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Citation Context ...performance gap seems to be wider for real, skewed data distributions. An additional, smaller contribution, is the derivation of (Eq. 3), From a practical point of view, it can help a query optimizer =-=[14]-=- give a good estimate for the cost of an R-tree index. Moreover, it makes the simulation analysis of R-trees easier and more reliable, eliminating the need to ask queries. Future research could examin... |

68 |
An Implementation and Performance Analysis of Spatial Data Access Methods
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Citation Context ... Figure 2: The file structure for the R-tree of the previous figure (fanout=3) the best trade-off between splitting time and search performance. Subsequent work on R-trees includes the work by Greene =-=[9]-=-, the R + -tree [26], R-trees using Minimum Bounding Polygons [16], and finally, the R -tree [3], which seems to have the best performance among the R-tree variants. The main idea in the R -tree is th... |

67 | P.: ‘Towards an Analysis of Range Query Performance - Pagel, Six, et al. - 1993 |

63 |
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Citation Context ...Hilbert curve can be generalized for higher dimensionalities. Algorithms to draw the two-dimensional curve of a given order, can be found in [10], [17]. An algorithm for higher dimensionalities is in =-=[5]-=-. The path of a space filling curve imposes a linear ordering on the grid points, which may be calculated by starting at one end of the curve and following the path to the other end. Figure 5 shows on... |

61 |
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Citation Context ...computer vision and robotics [2]; traditional databases, where a record with k attributes corresponds to a point in a k-d space; temporal databases, where time can be considered as one more dimension =-=[18]-=-; scientific databases, with spatial-temporal data, etc. Currently on sabbatical at IBM Almaden Research Center. This research was partially funded by the Systems Research Center (SRC) at the Universi... |

58 |
Optimization strategies for spatial query processing
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Citation Context ...vey can be found in [25]. These methods fall in the following broad classes: methods that transform rectangles into points in a higher dimensionality space [15]; methods that use linear quadtrees [8] =-=[1]-=- or, equivalently, the zordering [21] or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [23], hB-trees [19], cell-trees [11] e.t.c.) ... |

57 |
V.: ‘Spatial Search with Polyhedra
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Citation Context ...re (fanout=3) the best trade-off between splitting time and search performance. Subsequent work on R-trees includes the work by Greene [9], the R + -tree [26], R-trees using Minimum Bounding Polygons =-=[16]-=-, and finally, the R -tree [3], which seems to have the best performance among the R-tree variants. The main idea in the R -tree is the concept of forced re-insert, which is analog to the deferred-spl... |

42 |
Magic: A VLSI layout system
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Citation Context ...for the database management systems (DBMSs) of the near future is the ability to handle spatial data. Spatial data arise in many applications, including: Cartography [27]; Computer-Aided Design (CAD) =-=[22]-=- [12]; computer vision and robotics [2]; traditional databases, where a record with k attributes corresponds to a point in a k-d space; temporal databases, where time can be considered as one more dim... |

28 |
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Citation Context ...ess methods have been proposed. A recent survey can be found in [25]. These methods fall in the following broad classes: methods that transform rectangles into points in a higher dimensionality space =-=[15]-=-; methods that use linear quadtrees [8] [1] or, equivalently, the zordering [21] or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [2... |

24 |
Codes for Partial Match and Range Queries
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Citation Context ...visits all the points in a k-dimensional grid exactly once and never crosses itself. The Z-order (or Morton key order, or bit-interleaving, or Peano curve), the Hilbert curve, and the Gray-code curve =-=[6]-=- are examples of space filling curves. In [7], it was shown experimentally that the Hilbert curve achieves the best clustering among the three above methods. Next we provide a brief introduction to th... |

14 |
N-trees: Large ordered Indexes for Multi-dimensional Space
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Citation Context ...roduction One of the requirements for the database management systems (DBMSs) of the near future is the ability to handle spatial data. Spatial data arise in many applications, including: Cartography =-=[27]-=-; Computer-Aided Design (CAD) [22] [12]; computer vision and robotics [2]; traditional databases, where a record with k attributes corresponds to a point in a k-d space; temporal databases, where time... |

14 | Pfeffer A.: Generalized Search Trees for Database Systems - Hellerstein, Naughton - 1995 |

13 |
An Algorithm for Displaying a Class of Space-filling Curves
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Citation Context ...urve is a fractal, with a fractal dimension of 2 [20]. The Hilbert curve can be generalized for higher dimensionalities. Algorithms to draw the two-dimensional curve of a given order, can be found in =-=[10]-=-, [17]. An algorithm for higher dimensionalities is in [5]. The path of a space filling curve imposes a linear ordering on the grid points, which may be calculated by starting at one end of the curve ... |

13 |
New Features for Relational Database Systems to Support CAD Applications
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Citation Context ...he database management systems (DBMSs) of the near future is the ability to handle spatial data. Spatial data arise in many applications, including: Cartography [27]; Computer-Aided Design (CAD) [22] =-=[12]-=-; computer vision and robotics [2]; traditional databases, where a record with k attributes corresponds to a point in a k-d space; temporal databases, where time can be considered as one more dimensio... |

8 |
The Cell Tree: An Index for Geometric Data,’’ Memorandum No
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Citation Context ...trees [8] [1] or, equivalently, the zordering [21] or other space filling curves [7] [17]; and finally, methods based on trees (R-tree [13], k-d-trees [4], k-d-B-trees [23], hB-trees [19], cell-trees =-=[11]-=- e.t.c.) One of the most promising approaches in the last class is the R-tree [13]. It is the extension of the B-tree for multidimensional objects. A geometric object is represented by its minimum bou... |