Related papers: Space Efficient Linear Time Lempel-Ziv Factorizati…
Grammar compression is, next to Lempel-Ziv (LZ77) and run-length Burrows-Wheeler transform (RLBWT), one of the most flexible approaches to representing and processing highly compressible strings. The main idea is to represent a text as a…
One of the most famous and investigated lossless data-compression scheme is the one introduced by Lempel and Ziv about 40 years ago. This compression scheme is known as "dictionary-based compression" and consists of squeezing an input…
We present the first worst-case linear time algorithm that directly computes the parameterized suffix and LCP arrays for constant sized alphabets. Previous algorithms either required quadratic time or the parameterized suffix tree to be…
We show how to compress string dictionaries using the Lempel-Ziv (LZ78) data compression algorithm. Our approach is validated experimentally on dictionaries of up to 1.5 GB of uncompressed text. We achieve compression ratios often…
We introduce the first self-index based on the Lempel-Ziv 1977 compression format (LZ77). It is particularly competitive for highly repetitive text collections such as sequence databases of genomes of related species, software repositories,…
In this paper we consider the problem of computing the longest common abelian factor (LCAF) between two given strings. We present a simple $O(\sigma~ n^2)$ time algorithm, where $n$ is the length of the strings and $\sigma$ is the alphabet…
In this paper we propose a variant of the induced suffix sorting algorithm by Nong (TOIS, 2013) that computes simultaneously the Lyndon array and the suffix array of a text in $O(n)$ time using $\sigma + O(1)$ words of working space, where…
In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y.…
We introduce height-bounded LZ encodings (LZHB), a new family of compressed representations that are variants of Lempel-Ziv parsings with a focus on bounding the worst-case access time to arbitrary positions in the text directly via the…
The \emph{longest common extension} (\emph{LCE}) problem is to preprocess a given string $w$ of length $n$ so that the length of the longest common prefix between suffixes of $w$ that start at any two given positions is answered quickly. In…
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…
Let $L$ be a set of $n$ lines in the plane. The zone $Z(\ell)$ of a line $\ell$ in the arrangement $\mathcal{A}(L)$ of $L$ is the set of faces of $\mathcal{A}(L)$ whose closure intersects $\ell$. It is known that the combinatorial size of…
We describe how, given a text $T [1..n]$ and a positive constant $\epsilon$, we can build a simple $O (z \log n)$-space index, where $z$ is the number of phrases in the LZ77 parse of $T$, such that later, given a pattern $P [1..m]$, in $O…
Converting a compressed format of a string into another compressed format without an explicit decompression is one of the central research topics in string processing. We discuss the problem of converting the run-length Burrows-Wheeler…
We present a linear time and space algorithm computing the leftmost critical factorization of a given string on an unordered alphabet.
We show that the Longest Common Prefix Array of a text collection of total size n on alphabet [1, {\sigma}] can be computed from the Burrows-Wheeler transformed collection in O(n log {\sigma}) time using o(n log {\sigma}) bits of working…
Squares (fragments of the form $xx$, for some string $x$) are arguably the most natural type of repetition in strings. The basic algorithmic question concerning squares is to check if a given string of length $n$ is square-free, that is,…
An algorithm is given to factor an integer with $N$ digits in $\ln^m N$ steps, with $m$ approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a…
We give an $\mathcal{O}(n \log n)$-time, $\mathcal{O}(n)$-space algorithm for factoring a string into the minimum number of palindromic substrings. That is, given a string $S [1..n]$, in $\mathcal{O}(n \log n)$ time our algorithm returns…
We consider the communication complexity of the Hamming distance of two strings. Bille et al. [SPIRE 2018] considered the communication complexity of the longest common prefix (LCP) problem in the setting where the two parties have their…