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A General Theory for Deadlock Avoidance in Wormhole-Routed Networks

Author:
Eric Fleury  Pierre Fraigniaud  


Journal:
IEEE Trans. Parallel Distrib. Syst.


Abstract(summary):

Most machines of the last generation of distributed memory parallel computers possess speci c routers which are used to exchange messages between 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. In this paper, we describe a general theoretical framework for the study of deadlockfree routing functions. We give a general de nition of what can be a routing function. This de nition captures many speci c de nitions of the literature (e.g., vertexdependent, input-dependent, source-dependent, path-dependent, etc.). Using our de nition, we give a necessary and su cient condition which characterizes deadlock-free routing functions. Our theory embraces at a high level most of the theories related to deadlock avoidance in wormhole-routed networks previously derived in the literature. In particular, it applies not only to one-to-one routing, but also to one-to-many routing. The latter paradigm is used to solve the multicast problem with the path-based or tree-based facility.


Page:
626-638


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