E cient Self Simulation Algorithmsfor Recon gurable Arrays

There are several reconnguring-network models of parallel computation that are considered in the published literature, depending on their switching capabilities. Can these reconngurable models be the basis for the design of massively parallel computers? Perhaps the most fundamental related issue is virtual parallelism, or the self simulation problem: given an algorithm which is designed for a large reconngurable mesh, can it be executed eeciently on a smaller reconngurable mesh? In this work we give several positive answers to the self simulation problem. We show that the simulation of a reconnguring mesh by a smaller one can be carried optimally and using standard methods on the model in which buses are established along rows or along columns. A novel technique is shown to achieve asymptotically optimal self simulation on models which allow buses to switch column and row edges, provided that a bus is a \linear" path of connected edges. Finally, for models in which a bus is any sub-graph of the underlying mesh eecient simulations are presented, paying by an extra factor which is polylogarithmic in the size of the simulated mesh. Although the self simulation algorithms are complex and require extensive bookkeeping operations, the required space is asymptotically optimal.