A lower bound for parallel string matching

We present an Q(log log rn) lower bound on the number of rounds necessary for finding occurrences of a pattern string P[l. .rn] in a text string T[l ..2rn] in lparallel using m comparisons in each round. This is the first lower bound for this problem. The bound is within a constant factor of the fastest algorithm for this problem [BG] and also holds for an m-processor CRCW-PRAM in the case of a general alphabet. Consequently we derive the parallel complexity of the string matching problem using p processors for general alphabets which is, ● @(log logm) if &<P<m or in short Q( [~1 + log log(l+pi~l 2P).

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