Abstract
This paper presents and discusses a radically different approach to multi-dimensional indexing based on the concept of the space-filling curve. It reports the novel algorithms which had to be developed to create the first actual implementation of a system based on this approach, on some comparative performance tests, and on its actual use within the TriStarp Group at Birkbeck to provide a Triple Store repository. An important result that goes beyond this requirement, however, is that the performance improvement over the Grid File is greater the higher the dimension.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Theodore Bially. Space-Filling Curves: Their Generation and Their Application to Bandwidth Reduction. IEEE Transactions on Information Theory, IT-15(6):658–664, Nov 1969.
Arthur R. Butz. Alternative Algorithm for Hilbert’s Space-Filling Curve. IEEE Transactions on Computers, 20:424–426, April 1971.
Mir Derakhshan. A Development of the Grid File for the Storage of Binary Relations. PhD thesis, Birkbeck College, University of London, 1989.
Christos Faloutsos and Shari Roseman. Fractals for Secondary Key Retrieval. Technical Report UMIACS-TR-89-47, University of Maryland, 1989. http://www.cs.cmu.edu/christos/cpub.html.
Christos Faloutsos and Yi Rong. DOT: A Spatial Access Method Using Fractals. In: Proceedings of the Seventh International Conference on Data Engineering, April 8–12, 1991, Kobe, Japan, pages 152–159. IEEE Computer Society.
M. Freeston. The BANG File: A New Kind of Grid File. In: Umeshwar Dayal and Irving L. Traiger (eds): Proceedings of the Association for Computing Machinery Special Interest Group on Management of Data Annual Conference, May 27–29, 1987, San Francisco, California, pages 260–269. ACM Press.
Volker Gaede and Oliver Günther. Multidimensional Access Methods. ACM Computing Surveys, 30(2):170–231, June 1998.
Antonin Guttman. R-Trees: A Dynamic Index Structure for Spatial Seaching. In: SIGMOD’ 84: Proceedings of the Annual Meeting, volume 14(2) of SIGMOD Record, pages 47–57. ACM, 1984.
David Hilbert. Ueber stetige Abbildung einer Linie auf ein Flachenstuck. Mathematische Annalen. 38:459–460, 1891.
H.V. Jagadish. Analysis of the Hilbert curve for representing two-dimensional space. Information Processing Letters, 62(1):17–22, April 1997.
Akhil Kumar. A Study of Spatial Clustering Techniques. In: Dimitris Karagiannis (ed): Proceedings of the 5th International Conference on Database and Expert Systems Applications (DEXA’ 94), volume 856 of Lecture Notes in Computer Science, pages 57–71. Springer-Verlag, Sept 1994.
Jonathan Lawder. The Application of Space-Filling Curves to the Storage and Retrieval of Multi-dimensional Data (Submitted for PhD). Technical Report JL/1/99, Birkbeck College, University of London, 1999.
Bongki Moon and H.V. Jagadish and Christos Faloutsos and Joel H. Saltz. Analysis of the Clustering Properties of the Hilbert Space-Filling Curve. Tchnical Report CS-TR-3611 / UMIACS-TR-96-20, University of Maryland, 1996.
Jürg Nievergelt and Hans Hinterberger and Kenneth C. Sevcik. The Grid File: An Adaptable, Symmetric Multikey File Structure. ACM Transactions on Database Systems (TODS), 9(1):38–71, 1984.
Jack A. Orenstein and F.A. Manola. PROBE: Spatial Data Modeling and Query Processing in an Image Database Application. IEEE Transactions on Software Engineering, 14(5):611–629, 1988.
Giuseppe Peano. Sur une courbe, qui remplit toute une aire plane (On a curve which completely fills a planar region). Mathematische Annalen, 36:157–160, 1890.
Hans Sagan. Space-Filling Curves. Springer-Verlag, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lawder, J.K., King, P.J.H. (2000). Using Space-Filling Curves for Multi-dimensional Indexing. In: Lings, B., Jeffery, K. (eds) Advances in Databases. BNCOD 2000. Lecture Notes in Computer Science, vol 1832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45033-5_3
Download citation
DOI: https://doi.org/10.1007/3-540-45033-5_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67743-7
Online ISBN: 978-3-540-45033-7
eBook Packages: Springer Book Archive