Related papers: 2D Lyndon Words and Applications

These lecture notes provide an introduction to combinatorics on words and its interactions with dynamics, algebra, and arithmetic. The central theme is the notion of low factor complexity for infinite words. We investigate the following…

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…

Computing the LZ factorization (or LZ77 parsing) of a string is a computational bottleneck in many diverse applications, including data compression, text indexing, and pattern discovery. We describe new linear time LZ factorization…

The problem of storing a set of strings --- a string dictionary --- in compact form appears naturally in many cases. While classically it has represented a small part of the whole data to be processed (e.g., for Natural Language processing…

The size of the \textit{smallest suffixient set} of positions of a string recently emerged as a new measure of string \textit{repetitiveness} -- a measure reflecting how much of repetitive content the string contains. We study how to…

We propose an unsupervised neural model for learning a discrete embedding of words. Unlike existing discrete embeddings, our binary embedding supports vector arithmetic operations similar to continuous embeddings. Our embedding represents…

A string attractor of a string $T[1..|T|]$ is a set of positions $\Gamma$ of $T$ such that any substring $w$ of $T$ has an occurrence that crosses a position in $\Gamma$, i.e., there is a position $i$ such that $w = T[i..i+|w|-1]$ and the…

Lyndon factorization and Lempel-Ziv (LZ) factorization are both important tools for analysing the structure and complexity of strings, but their combinatorial structure is very different. In this paper, we establish the first direct…

Let $s$ be a finite sequence over a field of length $n$. It is well-known that if $s$ satisfies a linear recurrence of order $d$ with non-zero constant term, then the reverse of $s$ also satisfies a recurrence of order $d$ (with…

Convolutional neural network (CNN) is a neural network that can make use of the internal structure of data such as the 2D structure of image data. This paper studies CNN on text categorization to exploit the 1D structure (namely, word…

The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…

Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns.…

A two-dimensional configuration is a coloring of the infinite grid Z^2 with finitely many colors. For a finite subset D of Z^2, the D-patterns of a configuration are the colored patterns of shape D that appear in the configuration. The…

The work takes another look at the number of runs that a string might contain and provides an alternative proof for the bound. We also propose another stronger conjecture that states that, for a fixed order on the alphabet, within every…

A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in…

The problem of finding a center string that is `close' to every given string arises and has many applications in computational biology and coding theory. This problem has two versions: the Closest String problem and the Closest Substring…

Any permutation in the finite symmetric group can be written as a product of simple transpositions $s_i = (i~i+1)$. For a fixed permutation $\sigma \in \mathfrak{S}_n$ the products of minimal length are called reduced decompositions or…

Suffix trees are key and efficient data structure for solving string problems. A suffix tree is a compressed trie containing all the suffixes of a given text of length $n$ with a linear construction cost. In this work, we introduce an…

Pivoting methods are of vital importance for linear programming, the simplex method being the by far most well-known. In this paper, a primal-dual pair of linear programs in canonical form is considered. We show that there exists a sequence…

The anchor words algorithm performs provably efficient topic model inference by finding an approximate convex hull in a high-dimensional word co-occurrence space. However, the existing greedy algorithm often selects poor anchor words,…