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Multidimensional Declustering Schemes Using Golden Ratio and Kronecker Sequences
May/June 2003 (vol. 15 no. 3)
pp. 659-670

Abstract—We propose a new declustering scheme for allocating uniform multidimensional data among parallel disks. The scheme, aimed at reducing disk access time for range queries, is based on Golden Ratio Sequences for two dimensions and Kronecker Sequences for higher dimensions. Using exhaustive simulation, we show that, in two dimensions, the worst-case (additive) deviation of the scheme from the optimal response time for any range query is one when the number of disks (M) is at most 22; its worst-case deviation is two when M \leq 94; and its worst-case deviation is four when M \leq 550. In two dimensions, we prove that whenever M is a Fibonacci number, the average performance of the scheme is within 14 percent of the (generally, unachievable) strictly optimal scheme and its worst-case response time is within a multiplicative factor three of the optimal response time for any query, and within a factor 1.5 of the optimal for large queries. We also present comprehensive simulation results, on two-dimensional as well as on higher-dimensional data, that compare and demonstrate the advantages of our scheme over some recently proposed schemes in the literature.

[1] K. Abdel-Ghaffar and A.E. Abbadi, “Optimal Allocation of Two-Dimensional Data,” Proc. Int'l Conf. Database Theory, pp. 409-418, 1997.
[2] M.J. Atallah and S. Prabhakar, “(Almost) Optimal Parallel Block Access for Range Queries,” Proc. ACM Symp. Principles of Database Systems, pp. 205-215, 2000.
[3] A. Bar-Noy, R. Bhatia, J. Naor, and B. Schieber, “Minimizing Service and Operation Costs of Periodic Scheduling,” Proc. Ninth ACM-SIAM Symp. Discrete Algorithms (SODA '98), pp. 11-20, 1998.
[4] J. Beck, “Probabilistic Diophantine Approximation, I Kronecker Sequences,” Ann. Math., 1994.
[5] S. Berchtold, C. Böhm, B. Braunmüller, D. Keim, and H.-P. Kriegel, “Fast Parallel Similarity Search in Multimedia Databases,” Proc. ACM SIGMOD Int'l Conf. Management of Data, pp. 1-12, 1997.
[6] R. Bhatia, R.K. Sinha, and C.-M. Chen, “Declustering Using Golden Ratio Sequences,” Proc. Int'l Conf. Data Eng., pp. 271-280, 2000.
[7] R. Bhatia, R.K. Sinha, and C.-M. Chen, “Hierarchical Declustering Schemes for Range Queries,” Proc. Int'l Conf. Extending Database Technology, pp. 525-537, 2000.
[8] C. Chang, B. Moon, A. Acharya, C. Shock, A. Sussman, and J. Saltz, “Titan: A High-Performance Remote-Sensing Database,” Proc. Int'l Conf. Data Eng., pp. 375-384, 1997.
[9] C.-M. Chen, R. Bhatia, and R. Sinha, “Declustering Using Golden Ratio and Kronecker Sequences,” technical report, Applied Research, Telcordia Tech nologies, 2002.
[10] C.-M. Chen and C. Cheng, “From Discrepancy to Declustering: Near Optimal Multidimensional Declustering Strategies for Range Queries,” Proc. ACM Symp. Database Principles, pp. 29-38, 2002.
[11] C.-M. Chen and R. Sinha, “Analysis and Comparison of Declustering Schemes for Interactive Navigation Queries,” IEEE Trans. Knowledge and Data Eng., vol. 12, no. 5, pp. 763-778, 2000.
[12] L.T. Chen and D. Rotem, “Declustering Objects for Visualization,” Proc. Int'l Conf. Very Large Data Bases, pp. 85-96, 1993.
[13] H.C. Du and J.S. Sobolewski, "Disk Allocation for Product Files on Multiple Disk Systems," ACM Trans. Database Systems, vol. 7, Mar. 1982.
[14] C. Faloutsos and P. Bhagwat, “Declustering Using Fractals,” Proc. Int'l Conf. Parallel and Distributed Information Systems, pp. 18-25, 1993.
[15] M.T. Fang, R.C.T. Lee, and C.C. Chang, "The Idea of Declustering and its Applications," Proc. Int'l Conf. Very Large Databases, 1986.
[16] H. Ferhatosmanoglu, D. Agrawal, and A.E. Abbadi, “Concentric Hyperspaces and Disk Allocations for Fast Parallel Range Searching,” Proc. Int'l Conf. Data Eng., pp. 608-615, 1999.
[17] N.D. Gershon and C.G. Miller, “Dealing with the Data Deluge,” IEEE Spectrum, 1993.
[18] A. Itai and Z. Rosberg, “A Golden Ratio Control Policy for a Multiple-Access Channel,” IEEE Trans. Automatic Control, vol. 29, pp. 712-718, 1984.
[19] M.H. Kim and S. Pramanik, “Optimal File Distribution for Partial Match Retrieval,” Proc. ACM Int'l Conf. Management of Data, pp. 173-182, 1988.
[20] D. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching. Addison-Wesley, 1973.
[21] S. Kou, M. Winslett, Y. Cho, and J. Lee, “New GDM-Based Declustering Methods for Parallel Range Queries,” Proc. Int'l Database Eng. and Applications Symp., pp. 119-127, 1999.
[22] J. Li, J. Srivastava, and D. Rotem, “CMD: A Multidimensional Declustering Method for Parallel Database Systems,” Proc. Int'l Conf. Very Large Databases, pp. 3-14, 1992.
[23] D.R. Liu and S. Shekhar, “Partitioning Similarity Graphs: A Framework for Declustering Problems,” Information Systems, vol. 21, no. 6, pp. 475-496, 1996.
[24] Y.-L. Lo, K. Hua, and H. Young, “GeMDA: A Multidimensional Data Partitioning Technique for Multiprocessor Database Systems,” Distributed and Parallel Databases, vol. 9, no. 3, 2001. (A preliminary version appeared in DEXA 1997).
[25] J. Matousek, Geometric Discrepancy, an Illustrated Guide. Springer-Verlag, 1999.
[26] J.M. May, Parallel I/O for High Performance Computing. Morgan Kaufmann, 2001.
[27] B. Moon, A. Acharya, and J. Saltz, “Study of Scalable Declustering Algorithms for Parallel Grid Files,” Proc. Int'l Parallel Processing Symp., 1996.
[28] S. Prabhakar, personal communication, 2001.
[29] S. Prabhakar, K. Abdel-Ghaffar, D. Agrawal, and A.E. Abbadi, “Cyclic Allocation of Two-Dimensional Data,” Proc. Int'l Conf. Data Eng., 1998.
[30] S. Prabhakar, K. Abdel-Ghaffar, D. Agrawal, and A.E. Abbadi, “Efficient Retrieval of Multidimensional Datasets through Parallel I/O,” Proc. Fifth Int'l Conf. High Performance Computing, 1998.
[31] R.K. Sinha, R. Bhatia, and C.-M. Chen, “Asymptotically Optimal Declustering Schemes for 2-dim Range Queries,” Theoretical Computer Science, to appear. (A preliminary version appeared in Int'l Conf. Database Theory, 2001.).
[32] H. Weyl, “Uber die gleichverteilung von zahlem mod eins,” Math. Ann., 1916.
[33] Y. Zhou, S. Shekhar, and M. Coyle, "Disk Allocation Methods for Parallelizing Grid Files," Proc. 10th Int'l Conf. Data Eng., IEEE CS Press, 1994.

Index Terms:
Declustering, disk allocation, parallel databases.
Citation:
Chung-Min Chen, Randeep Bhatia, Rakesh K. Sinha, "Multidimensional Declustering Schemes Using Golden Ratio and Kronecker Sequences," IEEE Transactions on Knowledge and Data Engineering, vol. 15, no. 3, pp. 659-670, May-June 2003, doi:10.1109/TKDE.2003.1198397
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