This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Design of Efficient Regular Arrays for Matrix Multiplication by Two-Step Regularization
February 1995 (vol. 6 no. 2)
pp. 215-222

Abstract—A two-step regularization method in which first permutation sequences and then broadcast planes are selected is proposed to design various regular iterative algorithms for matrix multiplication. The regular iterative algorithms are then spacetime mapped to regular arrays, such as mesh, cylindrical, two-layered mesh, and orbital arrays. The proposed method can be used to design regular arrays with execution time of less than $N$ (problem size).

Index Terms—Broadcast, cylindrical array, mesh array, orbital array, parallel algorithm design, permutation sequence, propagation, two-layered mesh array, VLSI architecture

[1] H. T. Kung and C. E. Leiserson,“Systolic arrays for VLSI,”inProc. 1978 Soc. Indust., Appl. Math., 1979, pp. 256–282.
[2] S. Y. Kung,“VLSI array processor for signal processing,”inProc. Conf. Advanced Res. Integrat. Circuits, 1980.
[3] G. J. Li and B. W. Wah,“The design of optimal systolic arrays,”IEEE Trans. Comput., vol. C-34, Jan. 1985, pp. 66–77.
[4] W. A. Porter and J. L. Aravena,“Orbital architectures with dynamic reconfiguration,”inIEE Proc., vol. 134, Nov. 1987, pp. 281–287.
[5] W. A. Porter and J. L. Aravena,“Cylindrical arrays for matrix multiplication,”inProc. 24th Annu. Alleroton Conf. Commun., Control, Computing, Mar. 1988, pp. 595–602.
[6] S. C. Kak,“A two-layered mesh array for matrix multiplication,”Parallel Computing, vol. 6, pp. 383–385, 1988.
[7] J. C. Tsay and P. Y. Chang,“Some new designs of 2-D array for matrix multiplication and transitive closure,”IEEE Trans. Parallel, Distrib. Syst., to be published.
[8] H. V. Jagadish and T. Kailath,“A family of new efficient arrays for matrix multiplication,”IEEE Trans. Comput., vol. C-38, pp. 149–155, Jan. 1989.
[9] A. Benaini and Y. Robert,“An even faster systolic array for matrix multiplication,”Parallel Computing, vol. 12, pp. 249–254, 1989.
[10] S.K. Rao,“Regular iterative algorithms and their implementations on processor arrays,” PhD thesis, Stanford Univ., 1985.
[11] Y. Wong and J. M. Delosme,“Transformation of broadcasts into propagations in systolic algorithms,”J. Parallel Distrib. Comput., vol. 14, pp. 121–145, 1992.
[12] S.Y. Kung, VLSI Array Processors. Prentice Hall, 1988.

Citation:
Jong-Chuang Tsay, Pen-Yuang Chang, "Design of Efficient Regular Arrays for Matrix Multiplication by Two-Step Regularization," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 2, pp. 215-222, Feb. 1995, doi:10.1109/71.342137
Usage of this product signifies your acceptance of the Terms of Use.