Optimal Parallel Algorithms for Periods, Palindromes and Squares (Extended Abstract)

of results Optimal concurrent-read concurrent-write parallel algorithms for two problems are presented: Finding all the periods of a string. The period of a string can be computed by previous eecient parallel algorithms only if it is shorter than half of the length of the string. Our new algorithm computes all the periods in optimal O(loglog n) time, even if they are longer. The algorithm can be used to compute all initial palin-dromes of a string within the same bounds. Testing if a string is square-free. We present an optimal O(loglog n) time algorithm for testing if a string is square-free, improving the previous bound of O(log n) given by Apostolico 1] and Crochemore and Rytter 12]. We show matching lower bounds for the optimal parallel algorithms that solve the problems above on a general alphabet. The lower bounds for testing if a string is square-free and nding all initial palindromes are derived by a modiication of the lower bound for nding the period of a string 7].