Abstract
An optimal O(log log n) time concurrent-read concurrent-write parallel<br />algorithm for detecting all squares in a string is presented. A tight<br />lower bound shows that over general alphabets this is the fastest possible<br />optimal algorithm. When p processors are available the bounds become<br />Theta(n log n / p + log log 2p). The algorithm uses an optimal parallel<br />string-matching algorithm together with periodicity properties to locate<br />the squares within the input string.
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