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(z logN log-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 ≥ 4N is an integer that can be handled in constant time under word RAM model. Our index supports searching for a pattern P in T in O(|P|fA + log w log |P| log-M(logN + log |P| log-M) + occ logN) time and insertion/deletion of a substring of length y in O((y + logN log-M) log w logN log-M) time, where fA = O(min{log logM log log w log log logM , √ log w log log w}). Also, we propose a new spaceefficient LZ77 factorization algorithm for a given text of length N, which runs in O(NfA + z log w log3 N(log- N)2) time with O(w) working space.