The theoretical background for the design of deadlock-free adaptive routing algorithms for wormhole networks is developed. The author proposes some basic definitions and two theorems. These create the conditions to verify that an adaptive algorithm is deadlock-free, even when there are cycles in the channel dependency graph. Two design methodologies are also proposed. The first supplies algorithms with a high degree of freedom, without increasing the number of physical channels. The second methodology is intended for the design of fault-tolerant algorithms. Some examples are given to show the application of the methodologies. Simulations show the performance improvement that can be achieved by designing the routing algorithms with the new theory.
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