Practical Algorithms for Online Routing on SIMD Meshes

The problem of online routing on SIMD meshes arises when these processors are used for real-time analysis of sensory input. Existing algorithms|ones not making unrealistic hardware assumptions|use sorting as a subroutine and so, while asymptotically optimal, have running times at least 3 times greater (for likely array sizes) than the lower bound of 4n 4 communication steps. Dedicated router networks address this problem, but are costly and not available on all processors. We present a greedy algorithm with very low overhead based on wormhole routing, which can be modi ed to use broadcast buses and recon gurable broadcast buses to successively improve performance. While we prove a bad worst case, performance is usually at worst a small additive constant from optimal, and always within a factor of 2 for every communication pattern tried. We also show that preprocessing randomization can improve the reliabilty of this result. Other algorithms are presented: one takes advantage of communication where all packets must travel only a short distance; another uses broadcast buses to transmit packets, improving performance when communication is sparse. Finally, we present performance results of these algorithms with respect to increased path width and packet splitting.