Near-optimal message routing and broadcasting in faulty hypercubes

A distributed routing algorithm for faulty hypercubes is described. This algorithm uses a directed depth-first approach to find a path between the sender and receiver of a message whenever at least one non-faulty path exists. We show that, when an arbitrary number of elements of the hypercube can be faulty, the algorithm always routes messages using fewer than 2N hops, whereN is the number of nodes in the hypercube. This performance is shown to be within a factor of two of the optimal worst-case routing efficiency. Through foult simulations, we show that, even when up to half of the elements in the cube are faulty, complete the analysis, we prove that our algorithm is deadlock-free. Finally, we present two extensions of the algorithm. The first uses local storage to reduce the overhead of the algorithm while the second allows reliable broadcasting in the presence of an arbitrary number of faults.Supported in part by the National Science Foundation under Grant CCR-9010547.Supported in part by the National Science Foundation Instrumentation Grant CDA-8820627.