A Minimal Periods Algorithm with Applications

Kosaraju in “Computation of squares in a string” briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w |)-time the minimal kth power, with period of length larger than s, starting at each position in a word w for arbitrary exponent k ≥ 2 and integer s ≥ 0. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju’s original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.