Related papers: Faster fully compressed pattern matching by recomp…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
The most fundamental problem considered in algorithms for text processing is pattern matching: given a pattern $p$ of length $m$ and a text $t$ of length $n$, does $p$ occur in $t$? Multiple versions of this basic question have been…
Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to…
Given a set of pattern strings $\mathcal{P}=\{P_1, P_2,\ldots P_k\}$ and a text string $S$, the classic dictionary matching problem is to report all occurrences of each pattern in $S$. We study the dictionary problem in the compressed…
The convolution between a text string $S$ of length $N$ and a pattern string $P$ of length $m$ can be computed in $O(N \log m)$ time by FFT. It is known that various types of approximate string matching problems are reducible to…
In grammar-based compression a string is represented by a context-free grammar, also called a straight-line program (SLP), that generates only that string. We refine a recent balancing result stating that one can transform an SLP of size…
Countless variants of the Lempel-Ziv compression are widely used in many real-life applications. This paper is concerned with a natural modification of the classical pattern matching problem inspired by the popularity of such compression…
We present an algorithm for computing the Lyndon factorization of a string that is given in grammar compressed form, namely, a Straight Line Program (SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where $m$ is the…
The compressed indexing problem is to preprocess a string $S$ of length $n$ into a compressed representation that supports pattern matching queries. That is, given a string $P$ of length $m$ report all occurrences of $P$ in $S$. We present…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
Various grammar compression algorithms have been proposed in the last decade. A grammar compression is a restricted CFG deriving the string deterministically. An efficient grammar compression develops a smaller CFG by finding duplicated…
We consider a natural generalization of the classical pattern matching problem: given compressed representations of a pattern p[1..M] and a text t[1..N] of sizes m and n, respectively, does p occur in t? We develop an optimal linear time…
In this paper we present an application of a simple technique of local recompression, previously developed by the author in the context of compressed membership problems and compressed pattern matching, to word equations. The technique is…
We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string.…
We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses…
In this paper we present a simple linear-time algorithm constructing a context-free grammar of size O(g log(N/g)) for the input string, where N is the size of the input string and g the size of the optimal grammar generating this string.…
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,…
Given a string $T$ of length $N$, the goal of grammar compression is to construct a small context-free grammar generating only $T$. Among existing grammar compression methods, RePair (recursive paring) [Larsson and Moffat, 1999] is notable…
We consider the problem of decompressing the Lempel--Ziv 77 representation of a string $S$ of length $n$ using a working space as close as possible to the size $z$ of the input. The folklore solution for the problem runs in $O(n)$ time but…
Motivated by the imminent growth of massive, highly redundant genomic databases, we study the problem of compressing a string database while simultaneously supporting fast random access, substring extraction and pattern matching to the…