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In this paper, we present the following results: (1) We propose a new\emph{dynamic compressed index} of $O(w)$ space, that supports searching for apattern $P$ in the current text in $O(|P| f(M,w) + \log w \log |P| \log^* M(\log N + \log |P| \log^* M) + \mathit{occ} \log N)$ time andinsertion/deletion of a substring of length $y$ in $O((y+ \log N\log^* M)\log w\log N \log^* M)$ time, where $N$ is the length of the current text, $M$ is themaximum length of the dynamic text, $z$ is the size of the Lempel-Ziv77 (LZ77)factorization of the current text, $f(a,b) = O(\min \{ \frac{\log\log a\log\log b}{\log\log\log a}, \sqrt{\frac{\log b}{\log\log b}} \})$ and $w = O(z\log N \log^*M)$. (2) We propose a new space-efficient LZ77 factorizationalgorithm for a given text of length $N$, which runs in $O(N f(N,w') + z \logw' \log^3 N (\log^* N)^2)$ time with $O(w')$ working space, where $w' =O(z \logN \log^* N)$. (3) We propose a data structure of $O(w)$ space which supportslongest common extension (LCE) queries on the text in $O(\log N + \log \ell\log^* N)$ time, where $\ell$ is the output LCE length. On top of the abovecontributions, we show several applications of our data structures whichimprove previous best known results on grammar-compressed string processing.

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