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 sub-expression sharing algorithms, which can both solve the original problem directly in reasonable time and guarantee a minimum adder depth.

在这项工作中，我们提出了一种通过解决问题的转置形式然后转置解决方案来减轻加法器图算法潜在利益的方法。关键的贡献是获得受输入实现影响的，具有最少数量的级联加法器的转置实现的系统方法。这样，通过先对矩阵进行转置然后对解进行转置，即可解决乘积之和为特例的宽和低常数矩阵乘法问题，这些问题通常在使用加法器图算法时通常会非常耗时。示例显示，虽然转置问题的解的加法器深度与原始问题之间的关系并不直接，