A new toroidal multi-dimensional network

Abstract

We present a new multi-dimensional network architecture arranged in alternated regular mesh fashion (D-ARM) with toroidal boundaries. Each node of the D-ARM network has D incoming links and D outgoing links. The node address inside the network is represented by a D-dimensional vector, I=(i/sub D/, ..., i/sub 2/, i/sub 1/), whose entries assume no-negative integer values. Each of the D outgoing links in a given node is parallel to one coordinate axis of the D-dimensional orthogonal coordinate system. Therefore, each node has exactly one incoming link and one outgoing link in each dimension. The direction of an outgoing link can be crescent or decrescent with respect to the orientation of the coordinate axis. We establish the direction of a d/sup t/h dimensional outgoing link of a given node. Due to the global isotropy of the D-ARM network, a shortest path routing algorithm can be easily implemented. To evaluate the network performance, we calculate the mean transfer delay when the network running the shortest path routing algorithm.