A Necessary and Sufficient Condition for Deadlock-Free Adaptive Routing in Wormhole Networks

  • Authors:
  • José Duato

  • Affiliations:
  • -

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1995

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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.