On the communication complexity of generalized 2-D convolution on array processors

Several parallel convolution algorithms for array processors with N/sup 2/ processing elements (PEs) connected by mesh, hypercube, and shuffle-exchange topologies, respectively, are presented. The computation time complexity is the same for array processors with different interconnection networks. The communication time complexity, however, varies from network to network, and is the main focus. It is shown that by using inter-PE communication networks efficiently, each PE requires only a small local memory, many unnecessary data transmissions are eliminated, and the overall time complexity (including computation and communication) of algorithms is reduced to O(M/sup 2/).<>