Related papers: Computing Minimal Absent Words and Extended Bispec…
A string $w$ is called a minimal absent word (MAW) for a string $S$ if $w$ does not occur as a substring in $S$ and all proper substrings of $w$ occur in $S$. MAWs are well-studied combinatorial string objects that have potential…
A string $w$ is called a minimal absent word (MAW) for another string $T$ if $w$ does not occur (as a substring) in $T$ and any proper substring of $w$ occurs in $T$. State-of-the-art data structures for reporting the set $\mathsf{MAW}(T)$…
A string $w$ is called a minimal absent word (MAW) for another string $T$ if $w$ does not occur in $T$ but the proper substrings of $w$ occur in $T$. For example, let $\Sigma = \{\mathtt{a, b, c}\}$ be the alphabet. Then, the set of MAWs…
The compact directed acyclic word graph (CDAWG) is the minimal compact automaton that recognizes all the suffixes of a string. Classically the CDAWG has been implemented as an index of the string it recognizes, requiring $o(n)$ space for a…
The compact directed acyclic word graph (CDAWG) [Blumer et al. 1987] of a string is the minimal compact automaton that recognizes all the suffixes of the string. CDAWGs can be used for various string tasks including text pattern searching,…
The compact directed acyclic word graph (CDAWG) of a string $T$ of length $n$ takes space proportional just to the number $e$ of right extensions of the maximal repeats of $T$, and it is thus an appealing index for highly repetitive…
Minimal absent words (MAW) of a genomic sequence are subsequences that are absent themselves but the subwords of which are all present in the sequence. The characteristic distribution of genomic MAWs as a function of their length has been…
A substring $u$ of a string $T$ is called a minimal unique substring (MUS) of $T$ if $u$ occurs exactly once in $T$ and any proper substring of $u$ occurs at least twice in $T$. A string $w$ is called a minimal absent word (MAW) of $T$ if…
The directed acyclic word graph (DAWG) of a string $y$ of length $n$ is the smallest (partial) DFA which recognizes all suffixes of $y$ with only $O(n)$ nodes and edges. In this paper, we show how to construct the DAWG for the input string…
Given a string $T$, it is known that its suffix tree can be represented using the compact directed acyclic word graph (CDAWG) with $e_T$ arcs, taking overall $O(e_T+e_{{\overline{T}}})$ words of space, where ${\overline{T}}$ is the reverse…
An absent factor of a string $w$ is a string $u$ which does not occur as a contiguous substring (a.k.a. factor) inside $w$. We extend this well-studied notion and define absent subsequences: a string $u$ is an absent subsequence of a string…
The compact directed acyclic word graph (CDAWG) of a string $T$ is an index occupying $O(\mathsf{e})$ space, where $\mathsf{e}$ is the number of right extensions of maximal repeats in $T$. For highly repetitive datasets, the measure…
We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet $\Sigma$ of cardinality $\sigma$. We show that the set $\text{MAW}(T)$ of minimal absent words of a rooted (resp.…
Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string $T$ is…
Compact directed acyclic word graphs (CDAWGs) [Blumer et al. 1987] are a fundamental data structure on strings with applications in text pattern searching, data compression, and pattern discovery. Intuitively, the CDAWG of a string $T$ is…
In this paper, we propose a novel approach to combine \emph{compact directed acyclic word graphs} (CDAWGs) and grammar-based compression. This leads us to an efficient self-index, called Linear-size CDAWGs (L-CDAWGs), which can be…
In this paper, we present the first study of the computational complexity of converting an automata-based text index structure, called the Compact Directed Acyclic Word Graph (CDAWG), of size $e$ for a text $T$ of length $n$ into other text…
Given a string $w$, another string $v$ is said to be a subsequence of $w$ if $v$ can be obtained from $w$ by removing some of its letters; on the other hand, $v$ is called an absent subsequence of $w$ if $v$ is not a subsequence of $w$. The…
Detecting all the strings that occur in a text more frequently or less frequently than expected according to an IID or a Markov model is a basic problem in string mining, yet current algorithms are based on data structures that are either…
An absent word of a word y of length n is a word that does not occur in y. It is a minimal absent word if all its proper factors occur in y. Minimal absent words have been computed in genomes of organisms from all domains of life; their…