Adaptive source routing in high-speed networks

We study algorithms for adaptive source routing in high-speed networks, where some of the links are unreliable. Thus, the delivery of a single message to its destination may require trying several paths. Assuming a priori knowledge of the failure probabilities of links, our objective is to devise routing strategies which minimize the expected delivery cost of a single message. We describe optimal strategies for two cases: a tree-like network and a general serial/parallel topology. Whereas in the first case the greedy algorithm is shown to be optimal (i.e., it is best to try the paths by decreasing order of their success probabilities), there is no simple decision rule for the second case. However, using some properties of serial/parallel graphs, we show that an optimal strategy can be easily derived from a fixed sequence of paths. We give an algorithm, polynomial in the number of links, for finding this sequence. For a general network, we show that the problem of devising an optimal strategy can be solved in polynomial space and is #P-Hard, and that the minimal expected delivery cost in a given network is also hard to approximate. Finally, we show that for scenarios of adaptive source routing, the common greedy strategy is not even a constant approximation to the optimal strategy. (C) 1996 Academic Press, Inc.