Single Instruction Stream - Multiple Data Stream Machine Interconnection Network Design*

An SIMD machine must have an interconnection network to pass data between processing elements. We introduce a model of SIMD machines which allows a formal mathematical analysis and comparison of different interconnection networks. Five interconnection networks that have been proposed in the literature are defined in terms of our model. They include a network similar to the one used in the STARAN, a network similar to the one recommended by Feng to implement data manipulating functions, the Illiac IV network, and the Perfect Shuffle. The networks are evaluated in terms of the upper and lower bounds on the time required for each network to simulate the actions of the others. It is usually impractical to implement all the interconnections that may be needed by the machine to perform a large variety of computations, so the ability of a network to simulate other interconnections is important. The methods used to prove the lower bounds and to construct the simulation algorithms to demonstrate the upper bounds can be generalized and applied to the analysis of other networks.