An Optimal O(log log n) Time Parallel Algorithm for Detecting all Squares in a String

Abstract

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