A novel approach to multiple constant multiplication using minimum spanning trees

In this work a novel approach to multiple constant multiplication based on minimum spanning trees is proposed. Each required coefficient is assigned to a vertex in a graph. The vertices are connected with weighted edges, where each edge weight corresponds to the number of adders required to derive one of the coefficient from the previous. The graph can be used to solve for the minimum spanning tree, which leads to a realization with a small number of adders. The optimal minimum spanning tree can be found in polynomial time. It is also possible to add extra constraints to the spanning tree, such as limited out-degree (corresponds to fan-out) and limited tree height (corresponds to delay). These problems are harder to solve, but there are good heuristics available. It is shown by simulation that the performance of the proposed algorithm is comparable with recently published algorithms.