Efficient Algorithm for Multi-Dimensional Matrix Multiplication Operations Representation

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Satya Prakash
Anil K Ahlawat


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. 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. EKMR scheme has managed to successfully optimize the performance of the multi-dimensional array operations to
the nth dimension of the array. The basic concept EKMR is to transform the multi-dimensional 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 multidimensional
matrix multiplication operation which used the TMR scheme. The study encourages designing data parallel algorithms for multidimensional
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.


Keywords: Matrix multiplication Algorithm, EKMR, TMR.


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