Detecting regularities on grammar-compressed strings

Abstract

We solve the problems of detecting and counting various forms of regularities in a string represented as a Straight Line Program (SLP). Given an SLP of size n that represents a string s of length N, our algorithm computes all runs and squares in s in O(n3 h) time and O(n2) space, where h is the height of the derivation tree of the SLP. We also show an algorithm to compute all gapped-palindromes in O(n3 h + gnhlog N) time and O(n2) space, where g is the length of the gap. The key technique of the above solution also allows us to compute the periods and covers of the string in O(n2 h) time and O(nh(n + log2 N)) time, respectively. © 2013 Springer-Verlag.