Some combinatorial aspects of parallel algorithm design for matrix multiplication

Abstract

In this paper, some combinatorial characteristics of matrix multiplication on regular two-dimensional arrays are studied. From the studies, we 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, we find that there is a transformation procedure to transform a cylindrical array to a two-layered mesh array.