Flexible Routing Criteria for Circuit-Switched Hypercubes

Abstract

Circuit-switched communication has been increasingly used in hypercube multiprocessors. Reserve-and-hold strategy is commonly used to establish a circuit-switched path between a pair of nodes in the hypercube. With this strategy, a routing algorithm has to be designed with sufficient care to avoid deadlocks. A commonly used, deadlock-free routing algorithm for establishing a path between any two nodes in a hypercube is the e-cube routing algorithm. This algorithm is oblivious and allows only one shortest path between each source-destination pair and, hence, does not utilize the flexibility provided by the hypercube. In this paper, we propose a new set of routing criteria for circuit-switched hypercubes that exploit the flexibility provided by the hypercube. Our routing criteria are provably deadlock-free and route messages along shortest paths. The number of paths allowed by these criteria is more than one for most source-destination pairs. We show that the flexibility provided by our routing criteria can be used to limit the negative effects due to component failures. We derive the exact number of disrupted source-destination pairs in the presence of a single component failure. We then show that these numbers can be minimized using the proposed relabeling techniques. The performance of the routing criteria is evaluated using simulations. The results show that our criteria, if used effectively, lead to a significant improvement in performance over the e-cube routing strategy for non-uniform traffic. In addition, worst-case time complexity with respect to permutation routing is studied.