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Some Combinatorial Aspects of Parallel Algorithm Design for Matrix Multiplication
March 1992 (vol. 41 no. 3)
pp. 355-361

Some combinatorial characteristics of matrix multiplication on regular two-dimensional arrays are studied. From the studies, the authors are able to design many efficient varieties of the cylindrical array and the two-layered mesh array for matrix multiplication. To design a cylindrical array for matrix multiplication, a systematic design procedure is proposed. In this design procedure, Latin square (a special type of matrix) plays an important role. To design a two-layered mesh array, it is found that there is a transformation procedure to transform a cylindrical array to a two-layered mesh array.

[1] S. C. Kak, "Multilayered array computing," inProc. 20th Annu. Conf. Inform. Sci. Syst., Princeton, 1986, pp. 436-441.
[2] S. C. Kak, "A two-layered mesh array for matrix multiplication,"Parallel Comput., pp. 383-385, 1986.
[3] H. T. Kung, "Why systolic architectures?,"IEEE Comput. Mag., vol. 15, pp. 37-46, Jan. 1982.
[4] S. Y. Kung, "On supercomputing with systolic/wavefront array processors,"Proc. IEEE, vol. 72, pp. 867-884, July 1984.
[5] S.Y. Kung,VLSI Array Processors, Prentice Hall, Englewood Cliffs, N.J. 1988.
[6] C. L. Liu,Introduction to Combinatorial MathematicsNew York: McGraw-Hill, 1968, ch. 11.
[7] Y. J. Ma, J. F. Wang, and J. Y. Lee, "Systolic array mapping of sequential algorithm for VLSI architecture," inProc. Int. Comput. Symp., Tainan, Taiwan, R.O.C., 1986, pp. 865-874.
[8] W. A. Porter and J. L. Aravena, "Cylindrical arrays for matrix multiplication," inProc. 24th Annu. Allernton Conf. Commun., Contr. and Comput., Monticello, 1986, pp. 595-602.
[9] W. A. Porter and J. L. Aravena, "Orbital architectures with dynamic reconfiguration,"Proc. IEE, vol. 134, pt. E, no. 6, pp. 281-287, Nov. 1987.

Index Terms:
combinatorial aspects; parallel algorithm; matrix multiplication; two-dimensional arrays; cylindrical array; two-layered mesh array; Latin square; two-layered mesh array; transformation procedure; combinatorial mathematics; matrix algebra; parallel algorithms.
Jong-Chuang Tsay, Sy Yuan, "Some Combinatorial Aspects of Parallel Algorithm Design for Matrix Multiplication," IEEE Transactions on Computers, vol. 41, no. 3, pp. 355-361, March 1992, doi:10.1109/12.127449
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