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

Deadlock avoidance is a key issue in wormhole networks. A first approach [8] consists of removing the cyclic dependencies between channels. Although this 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 [12] 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 propose a necessary and sufficient condition for deadlock-free adaptive routing. This condition is the key for the design of maximally adaptive routing algorithms with minimum restrictions. Some examples are given, showing the application of the new theory. In particular, we propose a partially adaptive routing algorithm for k-ary n-cubes which doubles the throughput without increasing the hardware complexity significantly.