Dynamic index, LZ factorization, and LCE queries in compressed space

In this paper, we present the following results: (1) We propose a new dynamic compressed index of O(w) space, that supports searching for a pattern P in the current text in O(|P | logw+logw log |P | logN(log M)+occ logN) time and insertion/deletion of a substring of length y in O((y + logN log M) logw logN log M) time, where N is the length of the current text, M is the maximum length of the dynamic text, z is the size of the Lempel-Ziv77 (LZ77) factorization of the current text, and w = O(z logN log M). (2) We propose a new space-efficient LZ77 factorization algorithm for a given text of length N , which runs in O(N logw+z logw log N(log N)) time with O(w) working space, where w = O(z logN log N). (3) We propose a data structure of O(w) space which supports longest common extension (LCE) queries on the text in O(logN log N) time. The LCE data structure can also maintain a grammar-compressed representation of a dynamic text efficiently. On top of the above contributions, we show several applications of our data structures which improve previous known results.