The computation of the least lexicographic rotation of a string leads to the identification of polygon similarity. An O(logn) time CRCW PRAM algorithm for computing the least lexicographic rotation of a circular string (of length n) over a fixed alphabet is presented here. The logarithmic running time is achieved by using O(n/logn) processors and its space complexity is linear. A second algorithm for unbounded alphabets requires O(lognloglogn) units of time, uses O(n/logn) processors