Abstract
Declustering techniques have been widely adopted in parallel storage systems (e.g. disk arrays) to speed up bulk retrieval of multidimensional data. A declustering scheme distributes data items among multiple devices, thus enabling parallel I/O access and reducing query response time. We measure the performance of any declustering scheme as its worst case additive deviation from the ideal scheme. The goal thus is to design declustering schemes with as small an additive error as possible. We describe a number of declustering schemes with additive error O(log M) for 2-dimensional range queries, where M is the number of disks. These are the first results giving such a strong bound for any value of M. Our second result is a lower bound on the additive error. In 1997, Abdel-Ghaffar and Abbadi showed that except for a few stringent cases, additive error of any 2-dim declustering scheme is at least one. We strengthen this lower bound to Ω((log M)(d-1)/2) for d-dim schemes and to Ω(log M) for 2-dim schemes, thus proving that the 2-dim sche- mes described in this paper are (asymptotically) optimal. These results are obtained by establishing a connection to geometric discrepancy, a widely studied area of mathematics. We also present simulation results to evaluate the performance of these schemes in practice.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
K. Abdel-Ghaffar and A. E. Abbadi. Optimal allocation of two-dimensional data. In Proceedings of the International Conference on Database Theory, 1997.
M.J. Atallah and S. Prabhakar. (Almost) optimal parallel block access for range queries. In ACM Symp. on Principles of Database Systems, May 2000.
R. C. Baker. On irregularities of distribution, II. Journal of London Math. Soc.To appear.
S. Berchtold, C. Böhm, B. Braunmüller, D.A. Keim, and H.-P. Kriegel. Fast parallel similarity search in multimedia databases. In Proc. of ACM Int’l Conf. on Management of Data, 1997.
R. Bhatia, R. K. Sinha, and C. M. Chen. Declustering using golden ratio sequences.In 16th Int’l Conf. on Data Engineering, Feb 2000.
R. Bhatia, R. K. Sinha, and C. M. Chen. Hierarchical declustering schemes for range queries. In 7th Int’l Conf. on Extending Database Technology, Mar 2000.
C. Chang, B. Moon, A. Acharya, C. Shock, A. Sussman, and J. Saltz. Titan: a high-performance remote-sensing database. In 13th Int. Conf. on Data Engineering,1997.
C.M. Chen and R. Sinha. Raster-spatial data declustering revisited: an interactive navigation perspective. In 15th Int. Conf. on Data Engineering, 1999.
L.T. Chen and D. Rotem. Declustering objects for visualization. In Proc. of the 19th International Conference on Very Large Data Bases, 1993.
H.C. Du and J.S. Sobolewski. Disk allocation for cartesian product files on multiple disk systems. ACM Trans. Database Systems, pages 82–101, 1982.
C. Faloutsos and P. Bhagwat. Declustering using fractals. In Proceedings of the 2nd International Conference on Parallel and Distributed Information Systems, 1993.
H. Faure. Discrepancy of sequences associated with a number system (in dimensions) (in french). Acta Arithmetic, 41(4):337–351, 1982.
H. Faure. Good permutations for extreme discrepancy. J. Number Theory, 42:47–56, 1992.
H. Ferhatosmanoglu and D. Agrawal. Concentric hyperspaces and disk allocations for fast parallel range searching. In Proc. of 15th Int. Conf. on Data Engineering,pages 608–615, 1999.
E. Hlawka. The theory of uniform distribution. A B Academic Publ, Berkhamasted, Herts, 1984.
K. Keeton, D.A. Patterson, and J.M. Hellerstein. A case for intelligent disks (idisks). SIGMOD Record, 27(3), 1998.
M.H. Kim and S. Pramanik. Optimal file distribution for partial match retrieval. In Proceedings of the ACM International Conference on Management of Data, 1988.
S. Kou, M. Winslett, Y. Cho, and J. Lee. New gdm-based declustering methods for parallel range queries. In Int’l Database Engineering and Applications Symposium (IDEAS), Aug. 1999.
J. Matousek. Geometric discrepancy, an illustrated guide. Springer-Verlag, 1999.
B. Moon, A. Acharya, and J. Saltz. Study of scalable declustering algorithms for parallel grid files. In Proceedings of the 10th International Parallel Processing Symposium, 1996.
S. Prabhakar, K. Abdel-Ghaffar, D. Agrawal, and A. E. Abbadi. Cyclic allocation of two-dimensional data. In 14th Int. Conf. on Data Engineering, 1998.
S. Prabhakar, K. Abdel-Ghaffar, D. Agrawal, and A.E. Abbadi. Effcient retrieval of multidimensional datasets through parallel I/O. In 5th Int. Conf. on High Performance Computing, 1998.
I. M. Sobol. Distribution of points in a cube and approximate evaluation of integrals (in russian). Zh. Vychisl. Mat. i Mat. Fiz., 7:784–802, 1967.
J. G. van derCorput. Verteilungsfunktionen i. In Akad. Wetensch Amsterdam, pages 813–821, 1935.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sinha, R.K., Bhatia, R., Chen, CM. (2001). Asymptotically Optimal Declustering Schemes for Range Queries. In: Van den Bussche, J., Vianu, V. (eds) Database Theory — ICDT 2001. ICDT 2001. Lecture Notes in Computer Science, vol 1973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44503-X_10
Download citation
DOI: https://doi.org/10.1007/3-540-44503-X_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41456-8
Online ISBN: 978-3-540-44503-6
eBook Packages: Springer Book Archive