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A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks
October 1995 (vol. 6 no. 10)
pp. 1055-1067

Abstract—Deadlock avoidance is a key issue in wormhole networks. A first approach [8] consists of removing the cyclic dependencies between channels. Many deterministic and adaptive routing algorithms have been proposed based on that approach. Although the absence of cyclic dependencies is a necessary and sufficient condition for deadlock-free deterministic routing, it is only a sufficient condition for deadlock-free adaptive routing. A more powerful approach [11] only requires the absence of cyclic dependencies on a connected channel subset. The remaining channels can be used in almost any way. In this paper, we show that the previously mentioned approach is also a sufficient condition. Moreover, we propose a necessary and sufficient condition for deadlock-free adaptive routing. This condition is the key for the design of fully adaptive routing algorithms with minimum restrictions. An example shows the application of the new theory.

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Index Terms:
Adaptive routing, deadlock avoidance, multicomputers, virtual channels, wormhole.
Citation:
José Duato, "A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 10, pp. 1055-1067, Oct. 1995, doi:10.1109/71.473515
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