A General Theory for Deadlock Avoidance in Wormhole-Routed Networks

Article dans revue scientifique avec comité de lecture.Most of the machines from the last generation of distributed memory parallel computers possess specific routers that are used to communicate with non-neighboring nodes in the network. Among the several technologies, wormhole routing is usually prefered because it allows low channel-setup time and reduces the dependency between latency and inter-node distance. However, wormhole routing is very susceptible to deadlock because messages are allowed to hold many resources while requesting others. Therefore, designing deadlock-free routing algorithms using few hardware facilities is a major problem for wormhole-routed networks. Even though maximizing the degree of adaptiveness of a routing algorithm is not necessarily the best way to obtain the largest efficiency/complexity ratio, adding some adaptiveness improves the performance. It is therefore of great interest to answer the following question: given any network $G$ and any adaptive routing function R on G, is R deadlock-free or not? Characterizations of deadlock-free routing functions in terms of channel dependency graph have been known for a long time for deterministic routing, but only for a short time for adaptive routing, and only for some particular definitions of the routing functions. In this paper, we give a general framework to study deadlock-free routing functions. First we give a general definition that captures many specific definitions of the literature (namely vertex-dependent, input-dependent, source-dependent, path-dependent, etc.). With this general definition, we give a necessary and sufficient condition that characterizes deadlock-free routing functions for a large class of definitions. Using our results, we study several adaptive routing algorithms that have been proposed for meshes, and we derive a new algorithm that offers a higher degree of adaptiveness