Parallel recognition and parsing on the hypercube

The authors present parallel algorithms for recognizing and parsing context-free languages on the hypercube. This algorithm is both time-wise and space-wise optimal with respect to the usual sequential dynamic programming algorithm. Also, the number of nonoverlapping interprocessor data transmissions for the recognition phase is small. It is noted that this is desirable since communication cost in reality is a function of the number of transmissions as well as transmission length. The authors present another recognition algorithm that achieves the same time and space bounds but employs a dynamic loading balancing technique to increase processor utilization. The results of implementing these algorithms on a 64-node NCUBE/7 MIMD hypercube machine are also given. The experimental evidence indicates that, while both recognition algorithms exhibit acceptable speedups, using load balancing results in significantly better performance. The authors obtain parallel algorithms with the same time and space bounds as above for the polygon triangulation problem and the matrix product chain problem