相关论文: Vigemers: on the number of $k$-mers sharing the sa…

The minimizer of a word of size $k$ (a $k$-mer) is defined as its smallest substring of size $m$ (with $m\leq k$), according to some ordering on $m$-mers. minimizers have been used in bioinformatics -- notably -- to partition sequencing…

Minimizers are sampling schemes with numerous applications in computational biology. Assuming a fixed alphabet of size $\sigma$, a minimizer is defined by two integers $k,w\ge2$ and a linear order $\rho$ on strings of length $k$ (also…

Minimizer schemes, or just minimizers, are a very important computational primitive in sampling and sketching biological strings. Assuming a fixed alphabet of size $\sigma$, a minimizer is defined by two integers $k,w\ge2$ and a total order…

Minimizers sampling is one of the most widely-used mechanisms for sampling strings [Roberts et al., Bioinformatics 2004]. Let $S=S[1]\ldots S[n]$ be a string over a totally ordered alphabet $\Sigma$. Further let $w\geq 2$ and $k\geq 1$ be…

Minimizers sampling is one of the most widely-used mechanisms for sampling strings. Let $S=S[0]\ldots S[n-1]$ be a string over an alphabet $\Sigma$. In addition, let $w\geq 2$ and $k\geq 1$ be two integers and $\rho=(\Sigma^k,\leq)$ be a…

A major challenge in next-generation genome sequencing (NGS) is to assemble massive overlapping short reads that are randomly sampled from DNA fragments. To complete assembling, one needs to finish a fundamental task in many leading…

We initiate the study of computational problems on $k$-mers (strings of length $k$) in labeled graphs. As a starting point, we consider the problem of counting the number of distinct $k$-mers found on the walks of a graph. We establish that…

Motivation: Building the histogram of occurrences of every $k$-symbol long substring of nucleotide data is a standard step in many bioinformatics applications, known under the name of $k$-mer counting. Its applications include developing de…

For taxonomic classification, we are asked to index the genomes in a phylogenetic tree such that later, given a DNA read, we can quickly choose a small subtree likely to contain the genome from which that read was drawn. Although popular…

K-mer counting is a requisite process for DNA assembly because it speeds up its overall process. The frequency of K-mers is used for estimating the parameters of DNA assembly, error correction, etc. The process also provides a list of…

Background: Short sequence substrings of a fixed length k, called k-mers, are a ubiquitous computational primitive in bioinformatics, used across sequence indexing, read mapping, genome assembly, metagenomic classification, and comparative…

The minimizers sampling mechanism is a popular mechanism for string sampling introduced independently by Schleimer et al. [SIGMOD 2003] and by Roberts et al. [Bioinf. 2004]. Given two positive integers $w$ and $k$, it selects the…

The extraction of k-mers from sequencing reads is an important task in many bioinformatics applications, such as all DNA sequence analysis methods based on de Bruijn graphs. These methods tend to be more accurate when the used k-mers are…

Genetic sequencing has become an increasingly affordable and accessible source of genomic data in computational biology. This data is often represented as $k$-mers, i.e., strings of some fixed length $k$ with symbols chosen from a reference…

The utility of DNA sequence substrings (k-mers) in alignment-free phylogenetic classification, including that of bacteria and viruses, is increasingly recognized. However, its biological basis eludes many twenty-first century practitioners.…

The analysis of biological sequencing data has been one of the biggest applications of string algorithms. The approaches used in many such applications are based on the analysis of k-mers, which are short fixed-length strings present in a…

The wide array of currently available genomes display a wonderful diversity in size, composition and structure with many more to come thanks to several global biodiversity genomics initiatives starting in recent years. However, sequencing…

N-grams have been a common tool for information retrieval and machine learning applications for decades. In nearly all previous works, only a few values of $n$ are tested, with $n > 6$ being exceedingly rare. Larger values of $n$ are not…

Multi-parameter persistent homology is a recent branch of topological data analysis. In this area, data sets are investigated through the lens of homology with respect to two or more scale parameters. The high computational cost of many…

Many commonly studied species now have more than one chromosome-scale genome assembly, revealing a large amount of genetic diversity previously missed by approaches that map short reads to a single reference. However, many species still…