The classification of greedy algorithms
Science of Computer Programming
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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 modified to use broadcast buses and reconfigurable 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 realiability 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 increase path width and packet splitting.