A constant time optimal parallel algorithm for two-dimensional pattern matching

We give an alphabet-independent deterministic parallel algorithm for finding all occurrences of a pattern array of size mh x mw in a text array of size nh x nw in the concurrent-read-concurrent-write--parallel-random-access-machine (CRCW-PRAM) model. Our algorithm runs in O(1) time performing optimal, that is, O(nh x nw) work, following preprocessing of the pattern. This improves the previous best bound of O(log log m ) time with optimal work [A. Amir, G. Benson, and M. Farach, Proceedings 5th Annual ACM Symposium on Parallel Algorithms and Architectures, ACM, New York, 1993, pp. 79--85], following preprocessing of the pattern, where m = max{mh, mw}