Adaptive routing in k-ary n-cubes using incomplete diagnostic information

Abstract

In this paper, we present a fault-tolerant routing algorithm for k-ary n-cube interconnection networks which have become increasingly popular for the construction of massively parallel computers. The k-ary n-cube is a generalization of 2-ary hypercube network, and can model several interesting topologies such as the 2-d torus, 3-d torus, and the binary n-cube. In our routing algorithm, we assume that each node has static knowledge of the fault status of its immediate neighbours. Using this information, the nodes of the network execute a distributed diagnosis procedure whereby each node i learns the fault status of all other nodes that are reachable from i within k hops, k ⩾ 1. We refer to k as the diagnostic radius. Our simulation results indicate that a diagnostic radius larger than 1 can improve the performance of the routing algorithm. Our routing algorithm is a significant improvement over a similar algorithm due to Blough and Najand in that our algorithm does not place overheads on each message. The Blough-Najand algorithm requires each message to store the entire path from the source to destination, which can be quite large for a massively parallel multiprocessor. We compare the relative merits and demerits of our algorithm with those in the literature.