Finding All Periods and Initial Palindromes of a String in Parallel 1

An optimal O(log log n) time CRCW-PRAM algorithm for computing all period lengths of a string is presented. Previous parallel algorithms compute the period only if it is shorter than half of the length of the string. The algorithm can be used to nd all initial palindromes of a string in the same time and processor bounds. Both algorithms are the fastest possible over a general alphabet. We derive a lower bound for nding initial palindromes by modifying a known lower bound for nding the period length of a string [9]. When p processors are available the bounds become (dnpe+log logd1+p=ne 2p).