Hilbert R-tree: An Improved R-tree using Fractals.

@inproceedings{DBLP:conf/vldb/KamelF94,
  author    = {Ibrahim Kamel and
               Christos Faloutsos},
  editor    = {Jorge B. Bocca and
               Matthias Jarke and
               Carlo Zaniolo},
  title     = {Hilbert R-tree: An Improved R-tree using Fractals},
  booktitle = {VLDB'94, Proceedings of 20th International Conference on Very
               Large Data Bases, September 12-15, 1994, Santiago de Chile, Chile},
  publisher = {Morgan Kaufmann},
  year      = {1994},
  isbn      = {1-55860-153-8},
  pages     = {500-509},
  ee        = {db/conf/vldb/vldb94-500.html},
  crossref  = {DBLP:conf/vldb/94},
  bibsource = {DBLP, http://dblp.uni-trier.de}
}

Abstract

We propose a new R-tree structure that outperforms all the older ones. The heart of the idea is to facilitate the deferred splitting approach in R-trees. This is done by proposing an ordering on the R-tree nodes. This ordering has to be `good', in the sense that it should group `similar' data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs).

Following [Kamel93] we have chosen the so-called `2D-c' method, which sorts rectangles according to the Hilbert value of the center of the rectangles. Given the ordering, every node has a well-defined set of sibling nodes; thus, we can use deferred splitting. By adjusting the split policy, the Hilbert R-tree can achieve as high utilization as desired. To the contrary, the R*-tree has no control over the space utilization, typically achieving up to 70%. We designed the manipulation algorithms in detail, and we did a full implementation of the Hilbert R-tree. Our experiments show that the `2-to-3' split policy provides a compromise between the insertion complexity and the search cost, giving up to 28% savings over the R*-tree [Beckmann90] on real data.

Copyright © 1994 by the VLDB Endowment. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by the permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment.

Online Paper

• Download PDF file (www.vldb.org, Darmstadt, Germany)
• Download PDF file (www.acm.org, New York, USA)

ACM SIGMOD Anthology

• Windows: Click the letter of your CD drive
  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
• Mac: Click here
• UNIX/LINUX: mount the CD and click on the path of your mount point:
  /Anthology/vldb8997 or /cdrom

• Windows: Click the letter of your CD drive
  A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
• Mac: Click here
• UNIX/LINUX: mount the DVD and click on the path of your mount point:
  /Anthology/aDVD1 or /dvd

Printed Edition

References

[AS91]

Walid G. Aref, Hanan Samet: Optimization for Spatial Query Processing. VLDB 1991: 81-90 BibTeX

[BB82]

...

[Ben75]

Jon Louis Bentley: Multidimensional Binary Search Trees Used for Associative Searching. Commun. ACM 18(9): 509-517(1975) BibTeX

[Bia69]

T. Bially: Space-Filling Curves: Their Generation and Their Application to Bandwidth Reduction. IEEE Transactions on Information Theory 15(6): 658-664(1969) BibTeX

[BKSS90]

Norbert Beckmann, Hans-Peter Kriegel, Ralf Schneider, Bernhard Seeger: The R*-Tree: An Efficient and Robust Access Method for Points and Rectangles. SIGMOD Conference 1990: 322-331 BibTeX

[Fal88]

Christos Faloutsos: Gray Codes for Partial Match and Range Queries. IEEE Trans. Software Eng. 14(10): 1381-1393(1988) BibTeX

[FR89]

Christos Faloutsos, Shari Roseman: Fractals for Secondary Key Retrieval. PODS 1989: 247-252 BibTeX

[Fre87]

Michael Freeston: The BANG File: A New Kind of Grid File. SIGMOD Conference 1987: 260-269 BibTeX

[Gar82]

Irene Gargantini: An Effective Way to Represent Quadtrees. Commun. ACM 25(12): 905-910(1982) BibTeX

[Gra92]

...

[Gre89]

Diane Greene: An Implementation and Performance Analysis of Spatial Data Access Methods. ICDE 1989: 606-615 BibTeX

[Gri86]

J. G. Griffiths: An Algorithm for Displaying a Class of Space-filling Curves. Softw., Pract. Exper. 16(5): 403-411(1986) BibTeX

[Gun89]

Oliver Günther: The Design of the Cell Tree: An Object-Oriented Index Structure for Geometric Databases. ICDE 1989: 598-605 BibTeX

[Gut84a]

Antonin Guttman: New Features for Relational Database Systems to Support CAD Applications. Ph.D. thesis, University of California, Berkeley 1984
BibTeX

[Gut84b]

Antonin Guttman: R-Trees: A Dynamic Index Structure for Spatial Searching. SIGMOD Conference 1984: 47-57 BibTeX

[HN83]

Klaus Hinrichs, Jürg Nievergelt: The Grid File: A Data Structure to Support Proximity Queries on Spatial Objects. WG 1983: 100-113 BibTeX

[Jag90a]

H. V. Jagadish: Spatial Search with Polyhedra. ICDE 1990: 311-319 BibTeX

[Jag90b]

H. V. Jagadish: Linear Clustering of Objects with Multiple Atributes. SIGMOD Conference 1990: 332-342 BibTeX

[KF93]

Ibrahim Kamel, Christos Faloutsos: On Packing R-trees. CIKM 1993: 490-499 BibTeX

[KS91]

Curtis P. Kolovson, Michael Stonebraker: Segment Indexes: Dynamic Indexing Techniques for Multi-Dimensional Interval Data. SIGMOD Conference 1991: 138-147 BibTeX

[LS90]

David B. Lomet, Betty Salzberg: The hB-Tree: A Multiattribute Indexing Method with Good Guaranteed Performance. ACM Trans. Database Syst. 15(4): 625-658(1990) BibTeX

[Man77]

...

[OHM+84]

...

[Ore86]

Jack A. Orenstein: Spatial Query Processing in an Object-Oriented Database System. SIGMOD Conference 1986: 326-336 BibTeX

[RL85]

Nick Roussopoulos, Daniel Leifker: Direct Spatial Search on Pictorial Databases Using Packed R-Trees. SIGMOD Conference 1985: 17-31 BibTeX

[Rob81]

John T. Robinson: The K-D-B-Tree: A Search Structure For Large Multidimensional Dynamic Indexes. SIGMOD Conference 1981: 10-18 BibTeX

[Sam89]

Hanan Samet: The Design and Analysis of Spatial Data Structures. Addison-Wesley 1990
BibTeX

[SRF87]

Timos K. Sellis, Nick Roussopoulos, Christos Faloutsos: The R+-Tree: A Dynamic Index for Multi-Dimensional Objects. VLDB 1987: 507-518 BibTeX

[SSU91]

Abraham Silberschatz, Michael Stonebraker, Jeffrey D. Ullman: Database Systems: Achievements and Opportunities. Commun. ACM 34(10): 110-120(1991) BibTeX

[Whi81]

...

Referenced by

1. Gísli R. Hjaltason, Hanan Samet: Distance Browsing in Spatial Databases. ACM Trans. Database Syst. 24(2): 265-318(1999)
2. Botao Wang, Hiroyuki Horinokuchi, Kunihiko Kaneko, Akifumi Makinouchi: Parallel R-Tree Search Algorithm on DSVM. DASFAA 1999: 237-245
3. Volker Gaede, Oliver Günther: Multidimensional Access Methods. ACM Comput. Surv. 30(2): 170-231(1998)
4. Yván J. García, Mario A. Lopez, Scott T. Leutenegger: On Optimal Node Splitting for R-trees. VLDB 1998: 334-344
5. Rasa Bliujute, Christian S. Jensen, Simonas Saltenis, Giedrius Slivinskas: R-Tree Based Indexing of Now-Relative Bitemporal Data. VLDB 1998: 345-356
6. Apostolos Papadopoulos, Yannis Manolopoulos: Similarity Query Processing Using Disk Arrays. SIGMOD Conference 1998: 225-236
7. Jeffrey Scott Vitter: External Memory Algorithms. PODS 1998: 119-128
8. Pankaj K. Agarwal, Lars Arge, Jeff Erickson, Paolo Giulio Franciosa, Jeffrey Scott Vitter: Efficient Searching with Linear Constraints. PODS 1998: 169-178
9. Scott T. Leutenegger, Mario A. Lopez: The Effect of Buffering on the Performance of R-Trees. ICDE 1998: 164-171
10. Stefan Berchtold, Christian Böhm, Hans-Peter Kriegel: Improving the Query Performance of High-Dimensional Index Structures by Bulk-Load Operations. EDBT 1998: 216-230
11. Shashi Shekhar, Duen-Ren Liu: CCAM: A Connectivity-Clustered Access Method for Networks and Network Computations. IEEE Trans. Knowl. Data Eng. 9(1): 102-119(1997)
12. Euripides G. M. Petrakis, Christos Faloutsos: Similarity Searching in Medical Image Databases. IEEE Trans. Knowl. Data Eng. 9(3): 435-447(1997)
13. Viswanath Poosala, Yannis E. Ioannidis: Selectivity Estimation Without the Attribute Value Independence Assumption. VLDB 1997: 486-495
14. Nick Roussopoulos, Yannis Kotidis, Mema Roussopoulos: Cubetree: Organization of and Bulk Updates on the Data Cube. SIGMOD Conference 1997: 89-99
15. Apostolos Papadopoulos, Yannis Manolopoulos: Performance of Nearest Neighbor Queries in R-Trees. ICDT 1997: 394-408
16. Scott T. Leutenegger, J. M. Edgington, Mario A. Lopez: STR: A Simple and Efficient Algorithm for R-Tree Packing. ICDE 1997: 497-506
17. Kenneth C. Sevcik, Nick Koudas: Filter Trees for Managing Spatial Data over a Range of Size Granularities. VLDB 1996: 16-27
18. Flip Korn, Nikolaos Sidiropoulos, Christos Faloutsos, Eliot Siegel, Zenon Protopapas: Fast Nearest Neighbor Search in Medical Image Databases. VLDB 1996: 215-226
19. Yannis Theodoridis, Timos K. Sellis: A Model for the Prediction of R-tree Performance. PODS 1996: 161-171
20. Nick Koudas, Christos Faloutsos, Ibrahim Kamel: Declustering Spatial Databases on a Multi-Computer Architecture. EDBT 1996: 592-614
21. Christos Faloutsos: Fast Searching by Content in Multimedia Databases. IEEE Data Eng. Bull. 18(4): 31-40(1995)
22. Alberto Belussi, Christos Faloutsos: Estimating the Selectivity of Spatial Queries Using the `Correlation' Fractal Dimension. VLDB 1995: 299-310
23. Nick Roussopoulos, Stephen Kelley, Frédéic Vincent: Nearest Neighbor Queries. SIGMOD Conference 1995: 71-79
24. Christos Faloutsos, King-Ip Lin: FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets. SIGMOD Conference 1995: 163-174
25. King-Ip Lin, H. V. Jagadish, Christos Faloutsos: The TV-Tree: An Index Structure for High-Dimensional Data. VLDB J. 3(4): 517-542(1994)
26. Christos Faloutsos, Ibrahim Kamel: High Performance R-trees. IEEE Data Eng. Bull. 16(3): 28-33(1993)