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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.

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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.
Citation:
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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