Time-size tradeoffs for reconfigurable meshes

Many algorithms were devised for the reconfigurable mesh model (RN-mesh) for parallel computing which involve only a constant number of broadcasting steps. It was not known, however, how tight are the constants involved. Consider an n × n directed reconfigurable mesh (DRN-mesh) that computes a function f(n) in T steps, where T is a constant. In this paper we show that T can always be reduced to a single step, still using a polynomial size DRN-mesh. Furthermore, we show that this is in fact a general tradeoff: namely, the number of steps may be reduced to any value between 1 and T, paying by an exponential growth of the size of the DRN-mesh in the number of eliminated steps.