Related papers: Grammar-Compressed Indexes with Logarithmic Search…
The $r$-index (Gagie et al., JACM 2020) represented a breakthrough in compressed indexing of repetitive text collections, outperforming its alternatives by orders of magnitude. Its space usage, $\mathcal{O}(r)$ where $r$ is the number of…
In this work, we study the limits of compressed data structures, i.e., structures that support various queries on an input text $T\in\Sigma^n$ using space proportional to the size of $T$ in compressed form. Nearly all fundamental queries…
We introduce GCIS, a grammar compression algorithm based on the induced suffix sorting algorithm SAIS, introduced by Nong et al. in 2009. Our solution builds on the factorization performed by SAIS during suffix sorting. We construct a…
Data compression is very important feature in terms of saving the memory space. In this proposal, an indexed dictionary based compression is used for text data, where the word's reference in dictionary is used for compression. This approach…
In this paper, we propose a new \emph{dynamic compressed index} of $O(w)$ space for a dynamic text $T$, where $w = O(\min(z \log N \log^*M, N))$ is the size of the signature encoding of $T$, $z$ is the size of the Lempel-Ziv77 (LZ77)…
We present a data structure that stores a sequence $s[1..n]$ over alphabet $[1..\sigma]$ in $n\Ho(s) + o(n)(\Ho(s){+}1)$ bits, where $\Ho(s)$ is the zero-order entropy of $s$. This structure supports the queries \access, \rank\ and \select,…
We show that both the Lempel Ziv 77- and the 78-factorization of a text of length $n$ on an integer alphabet of size $\sigma$ can be computed in $O(n \lg \lg \sigma)$ time (linear time if we allow randomization) using $O(n \lg \sigma)$ bits…
Given two positions $i$ and $j$ in a string $T$ of length $N$, a longest common extension (LCE) query asks for the length of the longest common prefix between suffixes beginning at $i$ and $j$. A compressed LCE data structure is a data…
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 a pattern $P$ in the current text in $O(|P| f(M,w) + \log w \log |P| \log^* M (\log N + \log…
Like [1], we present an algorithm to compute the simulation of a query pattern in a graph of labeled nodes and unlabeled edges. However, our algorithm works on a compressed graph grammar, instead of on the original graph. The speed-up of…
A codec for compression of music signals is proposed. The method belongs to the class of transform lossy compression. It is conceived to be applied in the high quality recovery range though. The transformation, endowing the codec with its…
We revisit the classic border tree data structure [Gu, Farach, Beigel, SODA 1994] that answers the following prefix-suffix queries on a string $T$ of length $n$ over an integer alphabet $\Sigma=[0,\sigma)$: for any $i,j \in [0,n)$ return…
The string indexing problem is a fundamental computational problem with numerous applications, including information retrieval and bioinformatics. It aims to efficiently solve the pattern matching problem: given a text T of length n for…
Internal Pattern Matching (IPM) queries on a text $T$, given two fragments $X$ and $Y$ of $T$ such that $|Y|<2|X|$, ask to compute all exact occurrences of $X$ within $Y$. IPM queries have been introduced by Kociumaka, Radoszewski, Rytter,…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
Let $S_{T}(k)$ denote the set of distinct substrings of length $k$ in a string $T$, then the $k$-th substring complexity is defined by its cardinality $|S_{T}(k)|$. Recently, $\delta = \max \{ |S_{T}(k)| / k : k \ge 1 \}$ is shown to be a…
We describe a data structure that supports access, rank and select queries, as well as symbol insertions and deletions, on a string $S[1,n]$ over alphabet $[1..\sigma]$ in time $O(\lg n/\lg\lg n)$, which is optimal even on binary sequences…
We describe a compression-aware method to compute all-vs-all maximal exact matches (MEM) among strings of a repetitive collection $\mathcal{T}$. The key concept in our work is the construction of a fully-balanced grammar $\mathcal{G}$ from…
Binary jumbled pattern matching asks to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of length $i$ and has exactly $j$ 1-bits. This problem naturally generalizes to…
Let G be an embedded planar undirected graph that has n vertices, m edges, and f faces but has no self-loop or multiple edge. If G is triangulated, we can encode it using {4/3}m-1 bits, improving on the best previous bound of about 1.53m…