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1. GSearch: ultra-fast and scalable genome search by combining K-mer hashing with hierarchical navigable small world graphs

   https://doi.org/10.1093/nar/gkae609  

   Zhao, Jianshu; Both, Jean Pierre; Rodriguez-R, Luis M; Konstantinidis, Konstantinos T (July 2024, Nucleic Acids Research)

   Abstract Genome search and/or classification typically involves finding the best-match database (reference) genomes and has become increasingly challenging due to the growing number of available database genomes and the fact that traditional methods do not scale well with large databases. By combining k-mer hashing-based probabilistic data structures (i.e. ProbMinHash, SuperMinHash, Densified MinHash and SetSketch) to estimate genomic distance, with a graph based nearest neighbor search algorithm (Hierarchical Navigable Small World Graphs, or HNSW), we created a new data structure and developed an associated computer program, GSearch, that is orders of magnitude faster than alternative tools while maintaining high accuracy and low memory usage. For example, GSearch can search 8000 query genomes against all available microbial or viral genomes for their best matches (n = ∼318 000 or ∼3 000 000, respectively) within a few minutes on a personal laptop, using ∼6 GB of memory (2.5 GB via SetSketch). Notably, GSearch has an O(log(N)) time complexity and will scale well with billions of genomes based on a database splitting strategy. Further, GSearch implements a three-step search strategy depending on the degree of novelty of the query genomes to maximize specificity and sensitivity. Therefore, GSearch solves a major bottleneck of microbiome studies that require genome search and/or classification. 

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2. Compression algorithm for colored de Bruijn graphs

   https://doi.org/10.1186/s13015-024-00254-6  

   Rahman, Amatur; Dufresne, Yoann; Medvedev, Paul (December 2024, Algorithms for Molecular Biology)

   Abstract A colored de Bruijn graph (also called a set of k-mer sets), is a set of k-mers with every k-mer assigned a set of colors. Colored de Bruijn graphs are used in a variety of applications, including variant calling, genome assembly, and database search. However, their size has posed a scalability challenge to algorithm developers and users. There have been numerous indexing data structures proposed that allow to store the graph compactly while supporting fast query operations. However, disk compression algorithms, which do not need to support queries on the compressed data and can thus be more space-efficient, have received little attention. The dearth of specialized compression tools has been a detriment to tool developers, tool users, and reproducibility efforts. In this paper, we develop a new tool that compresses colored de Bruijn graphs to disk, building on previous ideas for compression of k-mer sets and indexing colored de Bruijn graphs. We test our tool, called ESS-color, on various datasets, including both sequencing data and whole genomes. ESS-color achieves better compression than all evaluated tools and all datasets, with no other tool able to consistently achieve less than 44% space overhead. The software is available athttp://github.com/medvedevgroup/ESSColor. 

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3. CMash: fast, multi-resolution estimation of k-mer-based Jaccard and containment indices

   https://doi.org/10.1093/bioinformatics/btac237  

   Liu, Shaopeng; Koslicki, David (June 2022, Bioinformatics)

   Abstract Motivation K-mer-based methods are used ubiquitously in the field of computational biology. However, determining the optimal value of k for a specific application often remains heuristic. Simply reconstructing a new k-mer set with another k-mer size is computationally expensive, especially in metagenomic analysis where datasets are large. Here, we introduce a hashing-based technique that leverages a kind of bottom-m sketch as well as a k-mer ternary search tree (KTST) to obtain k-mer-based similarity estimates for a range of k values. By truncating k-mers stored in a pre-built KTST with a large k=kmax value, we can simultaneously obtain k-mer-based estimates for all k values up to kmax. This truncation approach circumvents the reconstruction of new k-mer sets when changing k values, making analysis more time and space-efficient. Results We derived the theoretical expression of the bias factor due to truncation. And we showed that the biases are negligible in practice: when using a KTST to estimate the containment index between a RefSeq-based microbial reference database and simulated metagenome data for 10 values of k, the running time was close to 10× faster compared to a classic MinHash approach while using less than one-fifth the space to store the data structure. Availability and implementation A python implementation of this method, CMash, is available at https://github.com/dkoslicki/CMash. The reproduction of all experiments presented herein can be accessed via https://github.com/KoslickiLab/CMASH-reproducibles. Supplementary information Supplementary data are available at Bioinformatics online. 

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4. K-mer-based Approaches to Bridging Pangenomics and Population Genetics

   https://doi.org/10.1093/molbev/msaf047  

   Roberts, Miles D; Davis, Olivia; Josephs, Emily B; Williamson, Robert J (March 2025, Molecular Biology and Evolution)

   Harris, Kelley (Ed.)

   Abstract 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 lack multiple reference genomes and correctly aligning references to build pangenomes can be challenging for many species, limiting our ability to study this missing genomic variation in population genetics. Here, we argue that k-mers are a very useful but underutilized tool for bridging the reference-focused paradigms of population genetics with the reference-free paradigms of pangenomics. We review current literature on the uses of k-mers for performing three core components of most population genetics analyses: identifying, measuring, and explaining patterns of genetic variation. We also demonstrate how different k-mer-based measures of genetic variation behave in population genetic simulations according to the choice of k, depth of sequencing coverage, and degree of data compression. Overall, we find that k-mer-based measures of genetic diversity scale consistently with pairwise nucleotide diversity (π) up to values of about π=0.025 (R2=0.97) for neutrally evolving populations. For populations with even more variation, using shorter k-mers will maintain the scalability up to at least π=0.1. Furthermore, in our simulated populations, k-mer dissimilarity values can be reliably approximated from counting bloom filters, highlighting a potential avenue to decreasing the memory burden of k-mer-based genomic dissimilarity analyses. For future studies, there is a great opportunity to further develop methods to identifying selected loci using k-mers. 

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5. A near-tight lower bound on the density of forward sampling schemes

   https://doi.org/10.1093/bioinformatics/btae736  

   Kille, Bryce; Groot_Koerkamp, Ragnar; McAdams, Drake; Liu, Alan; Treangen, Todd J (December 2024, Bioinformatics)

   Ponty, Yann (Ed.)

   Abstract MotivationSampling k-mers is a ubiquitous task in sequence analysis algorithms. Sampling schemes such as the often-used random minimizer scheme are particularly appealing as they guarantee at least one k-mer is selected out of every w consecutive k-mers. Sampling fewer k-mers often leads to an increase in efficiency of downstream methods. Thus, developing schemes that have low density, i.e. have a small proportion of sampled k-mers, is an active area of research. After over a decade of consistent efforts in both decreasing the density of practical schemes and increasing the lower bound on the best possible density, there is still a large gap between the two. ResultsWe prove a near-tight lower bound on the density of forward sampling schemes, a class of schemes that generalizes minimizer schemes. For small w and k, we observe that our bound is tight when k≡1(mod w). For large w and k, the bound can be approximated by 1w+k⌈w+kw⌉. Importantly, our lower bound implies that existing schemes are much closer to achieving optimal density than previously known. For example, with the current default minimap2 HiFi settings w = 19 and k = 19, we show that the best known scheme for these parameters, the double decycling-set-based minimizer of Pellow et al. is at most 3% denser than optimal, compared to the previous gap of at most 50%. Furthermore, when k≡1(mod w) and the alphabet size σ goes to ∞, we show that mod-minimizers introduced by Groot Koerkamp and Pibiri achieve optimal density matching our lower bound. Availability and implementationMinimizer implementations: github.com/RagnarGrootKoerkamp/minimizers ILP and analysis: github.com/treangenlab/sampling-scheme-analysis. 

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