Faster Lyndon factorization algorithms for SLP and LZ78 compressed text

We present two efficient algorithms which, given a compressed representation of a string w of length N, compute the Lyndon factorization of w. Given a straight line program (SLP) S of size n that describes w, the first algorithm runs in O(n2+P(n,N)+Q(n,N)nlog⁡n) time and O(n2+S(n,N)) space, where P(n,N), S(n,N), Q(n,N) are respectively the pre-processing time, space, and query time of a data structure for longest common extensions (LCE) on SLPs. Given the Lempel-Ziv 78 encoding of size s for w, the second algorithm runs in O(slog⁡s) time and space.