Requirements for deadlock-free, adaptive packet routing

This paper studies the problem of deadlock-free packet routing in parallel and distributed architectures. Three main results are presented. First, it is shown that the standard technique of ordering the buffers so that every packet always has the possibility of moving to a higher-ordered buffer is not necessary for deadlock freedom. Second, it is shown that every deadlock-free, adaptive packet routing algorithm can be restricted, by limiting the adaptivity available, to obtain an oblivious algorithm which is also deadlock-free. Third, it is shown that any packet routing algorithm for a cycle or torus network which is free of deadlock and which uses only minimal length paths must require at least three buffers in some node. This matches the known upper bound of three buffers per node for deadlock-free, minimal packet routing on cycle and torus networks.