A Compressed Diagonals Remapping Technique for Dynamic Data Redistribution on Banded Sparse Matrix

  • Authors:

  • Ching-Hsien Hsu;Kun-Ming Yu

  • Affiliations:

  • Department of Computer Science and Information Engineering, Chung Hua University, Hsinchu, Taiwan 300, R.O.C. chh@chu.edu.tw;Department of Computer Science and Information Engineering, Chung Hua University, Hsinchu, Taiwan 300, R.O.C. yu@chu.edu.tw

  • Venue:
  • The Journal of Supercomputing
  • Year:
  • 2004

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Abstract

In many scientific applications, dynamic data redistribution is used to enhance algorithm performance and achieve data locality in parallel programs on distributed memory multi-computers. In this paper, we present a new method, Compressed Diagonals Remapping (CDR) technique aims to the efficiency of runtime 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 method can be applied to carry out data redistribution on the compressed diagonal matrix. This process is identical to redistribute data in the two-dimensional 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.