A tight lower bound on the number of channels required for deadlock-free wormhole routing

Wormhole routing is widely employed in current generation multicomputers and the design of deadlock-free wormhole routing algorithms is an important problem. In this note, we prove a tight lower bound on the number of channels required by a broad class of deadlockfree wormhole routing algorithms. This result has applications in proving that certain topologies do not admit deadlock-free wormhole routing algorithms, as well as applications in the design and analysis of fault-tolerant wormhole routing algorithms.