Related papers: Computing Matching Statistics on Repetitive Texts
We consider the problem of computing the Maximal Exact Matches (MEMs) of a given pattern $P[1 .. m]$ on a large repetitive text collection $T[1 .. n]$, which is represented as a (hopefully much smaller) run-length context-free grammar of…
Shannon's entropy is a definitive lower bound for statistical compression. Unfortunately, no such clear measure exists for the compressibility of repetitive strings. Thus, ad hoc measures are employed to estimate the repetitiveness of…
Unlike in statistical compression, where Shannon's entropy is a definitive lower bound, no such clear measure exists for the compressibility of repetitive sequences. Since statistical entropy does not capture repetitiveness, ad-hoc measures…
The problem of detecting and measuring the repetitiveness of one-dimensional strings has been extensively studied in data compression and text indexing. Our understanding of these issues has been significantly improved by the introduction…
The problem of finding factors of a text string which are identical or similar to a given pattern string is a central problem in computer science. A generalised version of this problem consists in implementing an index over the text to…
Document listing on string collections is the task of finding all documents where a pattern appears. It is regarded as the most fundamental document retrieval problem, and is useful in various applications. Many of the fastest-growing…
Adaptations of features commonly applied in the field of visual computing, co-occurrence matrix (COM) and run-length matrix (RLM), are proposed for the similarity computation of strings in general (words, phrases, codes and texts). The…
Let $S$ be a string of length $n$. In this paper we introduce the notion of \emph{string attractor}: a subset of the string's positions $[1,n]$ such that every distinct substring of $S$ has an occurrence crossing one of the attractor's…
We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…
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…
Repetitiveness measures reveal profound characteristics of datasets, and give rise to compressed data structures and algorithms working in compressed space. Alas, the computation of some of these measures is NP-hard, and straight-forward…
Detecting and measuring repetitiveness of strings is a problem that has been extensively studied in data compression and text indexing. However, when the data are structured in a non-linear way, like in the context of two-dimensional…
A weighted string over an alphabet of size $\sigma$ is a string in which a set of letters may occur at each position with respective occurrence probabilities. Weighted strings, also known as position weight matrices or uncertain sequences,…
Given an LZW/LZ78 compressed text, we want to find an approximate occurrence of a given pattern of length m. The goal is to achieve time complexity depending on the size n of the compressed representation of the text instead of its length.…
The notion of string attractor has been introduced in [Kempa and Prezza, 2018] in the context of Data Compression and it represents a set of positions of a finite word in which all of its factors can be "attracted". The smallest size…
We consider document listing on string collections, that is, finding in which strings a given pattern appears. In particular, we focus on repetitive collections: a collection of size $N$ over alphabet $[1,\sigma]$ is composed of $D$ copies…
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…
We present an online algorithm to deal with pattern matching in strings. The problem we investigate is commonly known as string matching with mismatches in which the objective is to report the number of characters that match when a pattern…
Advances in DNA sequencing mean databases of thousands of human genomes will soon be commonplace. In this paper we introduce a simple technique for reducing the size of conventional indexes on such highly repetitive texts. Given upper…
Given a text $T$ of length $n$ and a pattern $P$ of length $m$, the string matching problem is a task to find all occurrences of $P$ in $T$. In this study, we propose an algorithm that solves this problem in $O((n + m)q)$ time considering…