On Optimal Irregular Switch Box Designs

In this paper, we develop a unified theory in analyzing optimal switch box design problems, particularly for the unsolved irregular cases, where different pin counts are allowed on different sides. The results drawn from our system of linear Diophantine equations based formulation turn out to be general. We prove that the divideand-conquer (reduction) design methodology can also be applied to the irregular cases. Namely, an optimal arbitrarily large irregular or regular switch box can be obtained by combining small prime switch boxes, which largely reduces the design complexity. We revise the known VPR router for our experiments and show that the design optimality of switch boxes does pay off.