Improved multiple constant multiplication using a minimum spanning tree

Recently, a novel technique for the multiple constant multiplication (MCM) problem using minimum spanning trees (MSTs) has been proposed. The approach works by finding simple differences between the coefficients to realize and then applying the same method to the differences (which is an MCM problem as well). Each iteration is divided into two steps. First, finding a minimum spanning tree in the graph describing the differences between the coefficients. Second, as each edge in the graph may correspond to more than one difference, one difference is selected for each edge in the MST. Generally, both these stages have multiple solutions. The aim of this work is to more closely study how the MST and the differences should be selected to give better total results. It is also discussed how the two stages in each iteration may be joined into one problem.