Efficient self simulation algorithms for reconfigurable arrays

Perhaps the most basic question concerning a model for parallel computation is the self simulation problem: given an algorithm which is designed for a large machine, can it be executed efficiently on a smaller one? In this work we give several positive answers to the serf simulation problem on dynamically reconfigurable meshes. We show that the simulation of a reconfiguring mesh by a smaller one cast be carried optimally by using standard methods, on meshes such that buses axe 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 efficient 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.