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A New Approach for Representation of Multi- dimensional Matrix Multiplication Operations

In this paper, the extended Karnaugh Map representation (EKMR) scheme has been proposed as an alternative to the traditional matrix representation (TMR) which caused the multi-dimensional array operation to be inefficient when extended to dimensions higher than two. Multi-dimensional arrays are widely used in a lot of scientific studies but still some issues have been encountered regarding efficient operations of these multi-dimensional arrays. EKMR scheme has managed to successfully optimize the performance of the multi-dimensional array operations to the n th dimension of the array. The basic concept EKMR is to transform the multidimensional array in to a set of two-dimensional arrays. EKMR scheme implies Karnaugh Map which is a technique used to reduce a Boolean expression. It is commonly represented with the help of a rectangular map which holds all the possible values of the Boolean expression. Then the efficient data parallel algorithms for multi-dimensional matrix multiplication operation using EKMR are presented in this study which outperformed those data parallel algorithms for multi-dimensional matrix multiplication operation which used the TMR scheme. The study encourages designing data parallel algorithms for multi-dimensional dense and sparse multi-dimensional arrays for other operations as well using the EKMR scheme since this scheme produces the efficient performance for all dimensions and for all operations of the arrays.