Dynamic index and LZ factorization in compressed space

In this paper, we propose a new dynamic compressed index of O(w) space for a dynamic text T, where w=O(min(zlogNlog^∗M,N)) is the size of the signature encoding of T, z is the size of the Lempel–Ziv77 (LZ77) factorization of T, N is the length of T, and M≥N is the maximum length of T. Our index supports searching for a pattern P in T in O(|P|f_A+logwlog|P|log^∗M(logN+log|P|log^∗M)+occlogN) time and insertion/deletion of a substring of length y in O((y+logNlog^∗M)logwlogNlog^∗M) time, where occ is the number of occurrences of P in T and [Formula presented]. Also, we propose a new space-efficient LZ77 factorization algorithm for a given text T, which runs in O(Nf_A+zlogwlog³N(log^∗N)²) time with O(w) working space.