Percolation and anomalous transport as tools in analyzing parallel processing interconnection networks

It is quite apparent that much of the future advances in computation will be derived through the exploitation of parallel processing. Although a wide variety of topologies have been studied and proposed for both general-purpose and algorithm specific applications, there is still considerable discussion over which architectures are better and why. In this paper we discuss the application of percolation theory and anomalous transport to the issues of defective computer arrays. Percolation theory is used to discuss the static properties of the defective arrays and anomalous transport theory is used to discuss the dynamics of message passing on the defective array. It is hoped that exploiting these analogies will shed additional light on parallel processing issues.