Practical Algorithms for Online Routing on Fixed and Reconfigurable Meshes

Abstract The critical problem in creating practical online SIMD mesh routing algorithms is to minimize both the number of communication steps and the size and complexity of the queues required at each PE (processing element). Currently, the best available algorithms for likely array sizes require 16 n routing steps with queue size 1; if priority queues of size 2 q − 1 are allowed, the number of routing steps required is reduced to 14 n / q + 2 n . We present an algorithm (the MGRA), based on wormhole routing, that has routed a large number of communication patterns (all patterns tried besides a synthetically constructed worst case) in 5 n routing steps with a FIFO queue of size 2. We also show that the MGRA can be modified for meshes with broadcast buses and reconfigurable broadcast buses to route in a similar number of routing steps but with a queue size of 1. A second algorithm (the CGRA) uses reconfigurable broadcast buses in implementing cut-through routing. Using the CGRA, sparse patterns are routed in a small constant number of communication steps. We prove that the MGRA has bad worst case performance, but also show that a randomizing preprocessing step can improve the predictability of the original result. Finally, we show how performance scales with changing inter- and intra-PE path widths.