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The paper considers the power constrained design of orthogonal multiprocessor interconnection networks. The authors present a detailed model of message latency as a function of topology, technology architecture, and power. This model is then used to analyze a number of interesting scenarios, providing a sound engineering basis for interconnection network design in these cases. For example, they have observed that under a fixed power constraint, the network dimension which achieves minimal latency is a slowly growing function of system size. In addition, as they increase the available power per node for a fixed system size, the dimension at which message latency is minimized shifts towards higher dimensional networks.