:In this work, we present an approach to alleviate the potential benefit of adder graph algorithms by solving the transposed form of the
problem and then transposing the solution. The key contribution is a systematic way to obtain the transposed realization with a minimum
number of cascaded adders subject to the input realization. In this way, wide and low constant matrix multiplication problems, with sum of
products as a special case, which are normally exceptionally time consuming to solve using adder graph algorithms, can be solved by first
transposing the matrix and then transposing the solution. Examples show that while the relation between the adder depth of the solution to the
transposed problem and the original problem is not straightforward, there are many cases where the reduction in adder cost will more than
compensate for the potential increase in adder depth and result in implementations with reduced power consumption compared to using subexpression sharing algorithms, which can both solve the original problem directly in reasonable time and guarantee a minimum adder depth
Keywords: Constant matrix multiplication (CMM), Multiple constant multiplication (MCM),Shift-and-add, Sum of products (SOP),Minimum
depth expansion algorithm.