arXiv subjects

Camille Marchet

Publications and source records attributed to Camille Marchet.

8 recordsLinked to original sources

arXiv2026

Vigemers: on the number of $k$-mers sharing the same XOR-based minimizer

In bioinformatics, minimizers have become an inescapable method for handling $k$-mers (words of fixed size $k$) extracted from DNA or RNA sequencing, whether for sampling, storage, querying or partitioning. According to some fixed order on $m$-mers ($m<k$), the minimizer of a $k$-mer is defined as its smallest $m$-mer -- and acts as its fingerprint. Although minimizers are widely used for partitioning purposes, there is almost no theoretical work on the quality of the resulting partitions. For instance, it has been known for decades that the lexicographic order empirically leads to highly unbalanced partitions that are unusable in practice, but it was not until very recently that this observation was theoretically substantiated. The rejection of the lexicographic order has led the community to resort to (pseudo-)random orders using hash functions. In this work, we extend the theoretical results relating to the partitions obtained by the lexicographical order, departing from it to a (exponentially) large family of hash functions, namely where the $m$-mers are XORed against a fixed key. More precisely, provided a key $γ$ and a $m$-mer $w$, we investigate the function that counts how many $k$-mers admit $w$ as their minimizer (i.e. where $w\oplusγ$ is minimal among all $m$-mers of said $k$-mers). This number, denoted by $π_k^γ(w)$, represents the maximum size of the bucket associated with $w$, if all possible $k$-mers were to be seen and partitioned. We adapt the (lexicographical order) method of the literature to our framework and propose combinatorial equations that allow to compute, using dynamic programming, $π_k^γ(w)$ in $O(km^2)$ time and $O(km)$ space.

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arXiv2024

On the number of $k$-mers admitting a given lexicographical minimizer

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 datasets, binning together $k$-mers that share the same minimizer. It is folklore that using the lexicographical order lead to very unbalanced partitions, resulting in an abundant literature devoted to devising alternative orders for achieving better balanced partitions. To the best of our knowledge, the unbalanced-ness of lexicographical-based minimizer partitions has never been investigated from a theoretical point of view. In this article, we aim to fill this gap and determine, for a given minimizer, how many $k$-mers would admit the chosen minimizer -- i.e. what would be the size of the bucket associated to the chosen minimizer in the worst case, where all $k$-mers would be seen in the data. We show that this number can be computed in $O(km)$ space and $O(km^2)$ time. We further introduce approximations that can be computed in $O(k)$ space and $O(km)$ time. We also show on genomic datasets that the practical number of $k$-mers associated to a minimizer are closely correlated to the theoretical expected number. We introduce two conjectures that could help closely approximating the total number of $k$-mers sharing a minimizer. We believe that characterising the distribution of the number of $k$-mers per minimizer will help devise efficient lexicographic-based minimizer bucketting.

cs.DS↗

arXiv2024

Advances in practical k-mer sets: essentials for the curious

This paper provides a comprehensive survey of data structures for representing k-mer sets, which are fundamental in high-throughput sequencing analysis. It categorizes the methods into two main strategies: those using fingerprinting and hashing for compact storage, and those leveraging lexicographic properties for efficient representation. The paper reviews key operations supported by these structures, such as membership queries and dynamic updates, and highlights recent advancements in memory efficiency and query speed. A companion paper explores colored k-mer sets, which extend these concepts to integrate multiple datasets or genomes.

q-bio.GN↗

arXiv2024

Advances in colored k-mer sets: essentials for the curious

This paper provides a comprehensive review of recent advancements in k-mer-based data structures representing collections of several samples (sometimes called colored de Bruijn graphs) and their applications in large-scale sequence indexing and pangenomics. The review explores the evolution of k-mer set representations, highlighting the trade-offs between exact and inexact methods, as well as the integration of compression strategies and modular implementations. I discuss the impact of these structures on practical applications and describe recent utilization of these methods for analysis. By surveying the state-of-the-art techniques and identifying emerging trends, this work aims to guide researchers in selecting and developing methods for large scale and reference-free genomic data. For a broader overview of k-mer set representations and foundational data structures, see the accompanying article on practical k-mer sets.

q-bio.GN↗

arXiv2022

Sneak peek at the tig sequences: useful sequences built from nucleic acid data

This manuscript is a tutorial on tig sequences that emerged after the name "contig", and are of diverse purposes in sequence bioinformatics. We review these different sequences (unitigs, simplitigs, monotigs, omnitigs to cite a few), give intuitions of their construction and interest, and provide some examples of applications.

q-bio.OT↗

arXiv2017

A resource-frugal probabilistic dictionary and applications in bioinformatics

Indexing massive data sets is extremely expensive for large scale problems. In many fields, huge amounts of data are currently generated, however extracting meaningful information from voluminous data sets, such as computing similarity between elements, is far from being trivial. It remains nonetheless a fundamental need. This work proposes a probabilistic data structure based on a minimal perfect hash function for indexing large sets of keys. Our structure out-compete the hash table for construction, query times and for memory usage, in the case of the indexation of a static set. To illustrate the impact of algorithms performances, we provide two applications based on similarity computation between collections of sequences, and for which this calculation is an expensive but required operation. In particular, we show a practical case in which other bioinformatics tools fail to scale up the tested data set or provide lower recall quality results.

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arXiv2016

A resource-frugal probabilistic dictionary and applications in (meta)genomics

Genomic and metagenomic fields, generating huge sets of short genomic sequences, brought their own share of high performance problems. To extract relevant pieces of information from the huge data sets generated by current sequencing techniques, one must rely on extremely scalable methods and solutions. Indexing billions of objects is a task considered too expensive while being a fundamental need in this field. In this paper we propose a straightforward indexing structure that scales to billions of element and we propose two direct applications in genomics and metagenomics. We show that our proposal solves problem instances for which no other known solution scales-up. We believe that many tools and applications could benefit from either the fundamental data structure we provide or from the applications developed from this structure.

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arXiv2014

Navigating in a sea of repeats in RNA-seq without drowning

The main challenge in de novo assembly of NGS data is certainly to deal with repeats that are longer than the reads. This is particularly true for RNA- seq data, since coverage information cannot be used to flag repeated sequences, of which transposable elements are one of the main examples. Most transcriptome assemblers are based on de Bruijn graphs and have no clear and explicit model for repeats in RNA-seq data, relying instead on heuristics to deal with them. The results of this work are twofold. First, we introduce a formal model for repre- senting high copy number repeats in RNA-seq data and exploit its properties for inferring a combinatorial characteristic of repeat-associated subgraphs. We show that the problem of identifying in a de Bruijn graph a subgraph with this charac- teristic is NP-complete. In a second step, we show that in the specific case of a local assembly of alternative splicing (AS) events, we can implicitly avoid such subgraphs. In particular, we designed and implemented an algorithm to efficiently identify AS events that are not included in repeated regions. Finally, we validate our results using synthetic data. We also give an indication of the usefulness of our method on real data.

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