Abstract
In this paper, we present a new method, Compressed Diagonals Remapping (CDR) technique aims to the efficiency of data redistribution on banded sparse matrices. The main idea of the proposed technique is first to compress the source matrix into a Compressed Diagonal Matrix (CDM) form. Based on the compressed diagonal matrix, a one-dimensional local and global index transformation can be carried out to perform data redistribution on the compressed diagonal matrix, which is identical to redistribute data in the banded sparse matrix. The CDR technique uses an efficient one-dimensional indexing scheme to perform data redistribution on banded sparse matrix. A significant improvement of this approach is that a processor does not need to determine the complicated sending or receiving data sets for dynamic data redistribution. The indexing cost is reduced significantly. The second advantage of the present techniques is the achievement of optimal packing/unpacking stages consequent upon the consecutive attribute of column elements in a compressed diagonal matrix. Another contribution of our methods is the ability to handle sparse matrix redistribution under two disjoint processor grids in the source and destination phases. A theoretical model to analyze the performance of the proposed technique is also presented in this paper. To evaluate the performance of our methods, we have implemented the present techniques on an IBM SP2 parallel machine along with the v2m algorithm and a dense redistribution strategy. The experimental results show that our technique provides significant improvement for runtime data redistribution of banded sparse matrices in most test samples.
This work was partially supported by the NSC of ROC under contract NSC91-2213-E-252-001.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
R. Asenjo, L. F. Romero, M. Ujaldon and E. L. Zapata, “Sparse Block and Cyclic Data Distributions for Matrix Computations”, Proceedings of Adv. Workshop in High Performance Computing: Technology, Methods and Applications, pp. 359–377, June 1994.
G. Bandera and E.L. Zapata, “Sparse Matrix Block-Cyclic Redistribution,” In Proceeding of IEEE Int’l. Parallel Processing Symposium (IPPS’99), San Juan, Puerto Rico, April, 1999.
S. Chatterjee, J. R. Gilbert, F. J. E. Long, R. Schreiber, and S.-H. Teng, “Generating Local Address and Communication Sets for Data Parallel Programs,” Journal of Parallel and Distributed Computing, Vol. 26, pp. 72–84, 1995.
Frederic Desprez, Jack Dongarra, and Antoine Petitet, “Scheduling Block-Cyclic Data redistribution,” IEEE Trans. on PDS, vol. 9, no. 2, pp. 192–205, Feb. 1998.
I. Duff, R. Grimes, and J. Lewis, “Sparse matrix test problems,” ACM Trans. Math. Soft., 15, pp. 1–14, 1989.
S. K. S. Gupta, S. D. Kaushik, C.-H. Huang, and P. Sadayappan, “On Compiling Array Expressions for Efficient Execution on Distributed-Memory Machines,” JPDC, Vol. 32, pp. 155–172, 1996.
S. Hiranandani, K. Kennedy, J. Mellor-Crammey, and A. Sethi, “Compilation technique for block-cyclic distribution,” In Proc. ACM ICS, pp. 392–403, 1994.
C.-H Hsu, S.-W Bai, Y.-C Chung, C.-S Yang, “A Generalized Basic-Cycle Calculation Method for Efficient Array Redistribution,” IEEE Trans. on PDS, Vol. 11, No. 12, pp. 1201–1216, Dec. 2000.
C.-H Hsu, Y.-C Chung and C.-R Dow, “Efficient Methods for Multidimensional Array Redistribution,” The Journal of Supercomputing, Vol. 17, No. 1, 2000.
Ching-Hsien Hsu, “Optimization of sparse matrix redistribution on Multicomputers”, Proceedings of ICPP Workshops on Compiler and Runtime Techniques for Parallel Computing, Aug. 2002.
Edgar T. Kalns, and Lionel M. Ni, “Processor Mapping Technique Toward Efficient Data Redistribution,” IEEE Trans. on PDS, vol. 6, no. 12, Dec. 1995.
S. D. Kaushik, C. H. Huang, J. Ramanujam and P. Sadayappan, “Multiphase data redistribution: Modeling and evaluation,” Proceeding of IPPS’95, pp. 441–445.
Neungsoo Park, Viktor K. Prasanna, Cauligi S. Raghavendra, “Efficient Algorithms for Block-Cyclic Data redistribution Between Processor Sets,” IEEE Trans. on PDS, vol. 10, No. 12, pp.1217–1240, Dec. 1999.
Antoine P. Petitet, Jack J. Dongarra, “Algorithmic Redistribution Methods for Block-Cyclic Decompositions,” IEEE Trans. on PDS, vol. 10, no. 12, 1999.
L. Prylli and B. Touranchean, “Fast runtime block cyclic data redistribution on multiprocessors,” JPDC, vol. 45, pp. 63–72, Aug. 1997.
L. F. Romero and E. L. Zapata, “Data Distributions for Sparse Matrix Vector Multiplication”, Parallel Computing, vol. 21, no. 4, pp. 583–605, April 1995.
S. Ramaswamy, B. Simons, and P. Banerjee, “Optimization for Efficient Data redistribution on Distributed Memory Multicomputers,” JPDC, Vol. 38, 1996.
Rajeev. Thakur, Alok. Choudhary, and J. Ramanujam, “Efficient Algorithms for Data redistribution,” IEEE Trans. on PDS, vol. 7, no. 6, June 1996.
M. Ujaldón, E.L. Zapata, S.D. Sharma and J. Saltz, “Parallelization Techniques for Sparse Matrix Applications,” JPDC, vol. 38, no. 2, pp. 256–266, Nov. 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hsu, CH., Yu, KM. (2003). A Compressed Diagonals Remapping Technique for Dynamic Data Redistribution on Banded Sparse Matrix. In: Guo, M., Yang, L.T. (eds) Parallel and Distributed Processing and Applications. ISPA 2003. Lecture Notes in Computer Science, vol 2745. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37619-4_8
Download citation
DOI: https://doi.org/10.1007/3-540-37619-4_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40523-8
Online ISBN: 978-3-540-37619-4
eBook Packages: Springer Book Archive