Tradeo s Between Size and Time in Recon gurable MeshesYosi

The reconngurable mesh model (RN-mesh) for parallel computations exhibits some \strong" results of algorithms involving a constant number of broadcasting steps. Naturally, one can ask whether or not these constants are tight. Consider an nn directed reconngurable mesh (DRN-mesh) that computes a function f(n) in a constant number of steps T (directed indicates that the edges of the mesh are directed so that signals (at a given edge) ow in one direction only). In this paper we show that T can always be reduced to a single step, still using a polynomial size DRN-mesh (n 2 T). Moreover, we show that this is in fact a general tradeoo, i.e., by expanding the size of the DRN-mesh, one can reduce the number of steps to any value between 1 and T. We also show that this size expansion can be further reduced, when f is a composition of functions.