Designing efficient randstrobes for sequence similarity analyses.

MOTIVATION: Substrings of length k, commonly referred to as k-mers, play a vital role in sequence analysis. However, k-mers are limited to exact matches between sequences leading to alternative constructs. We recently introduced a class of new constructs, strobemers, that can match across substitutions and smaller insertions and deletions. Randstrobes, the most sensitive strobemer proposed in Sahlin (Effective sequence similarity detection with strobemers. Genome Res 2021a;31:2080-94. https://doi.org/10.1101/gr.275648.121), has been used in several bioinformatics applications such as read classification, short-read mapping, and read overlap detection. Recently, we showed that the more pseudo-random the behavior of the construction (measured in entropy), the more efficient the seeds for sequence similarity analysis. The level of pseudo-randomness depends on the construction operators, but no study has investigated the efficacy. RESULTS: In this study, we introduce novel construction methods, including a Binary Search Tree-based approach that improves time complexity over previous methods. To our knowledge, we are also the first to address biases in construction and design three metrics for measuring bias. Our evaluation shows that our methods have favorable speed and sampling uniformity compared to existing approaches. Lastly, guided by our results, we change the seed construction in strobealign, a short-read mapper, and find that the results change substantially. We suggest combining the two results to improve strobealign's accuracy for the shortest reads in our evaluated datasets. Our evaluation highlights sampling biases that can occur and provides guidance on which operators to use when implementing randstrobes. AVAILABILITY AND IMPLEMENTATION: All methods and evaluation benchmarks are available in a public Github repository at https://github.com/Moein-Karami/RandStrobes. The scripts for running the strobealign analysis are found at https://github.com/NBISweden/strobealign-evaluation.

Locality-preserving minimal perfect hashing of k-mers.

MOTIVATION: Minimal perfect hashing is the problem of mapping a static set of n distinct keys into the address space {1,…,n} bijectively. It is well-known that n log 2(e) bits are necessary to specify a minimal perfect hash function (MPHF) f, when no additional knowledge of the input keys is to be used. However, it is often the case in practice that the input keys have intrinsic relationships that we can exploit to lower the bit complexity of f. For example, consider a string and the set of all its distinct k-mers as input keys: since two consecutive k-mers share an overlap of k-1 symbols, it seems possible to beat the classic log 2(e) bits/key barrier in this case. Moreover, we would like f to map consecutive k-mers to consecutive addresses, as to also preserve as much as possible their relationship in the codomain. This is a useful feature in practice as it guarantees a certain degree of locality of reference for f, resulting in a better evaluation time when querying consecutive k-mers. RESULTS: Motivated by these premises, we initiate the study of a new type of locality-preserving MPHF designed for k-mers extracted consecutively from a collection of strings. We design a construction whose space usage decreases for growing k and discuss experiments with a practical implementation of the method: in practice, the functions built with our method can be several times smaller and even faster to query than the most efficient MPHFs in the literature.

Sparse and skew hashing of K-mers.

MOTIVATION: A dictionary of k-mers is a data structure that stores a set of n distinct k-mers and supports membership queries. This data structure is at the hearth of many important tasks in computational biology. High-throughput sequencing of DNA can produce very large k-mer sets, in the size of billions of strings-in such cases, the memory consumption and query efficiency of the data structure is a concrete challenge. RESULTS: To tackle this problem, we describe a compressed and associative dictionary for k-mers, that is: a data structure where strings are represented in compact form and each of them is associated to a unique integer identifier in the range [0,n). We show that some statistical properties of k-mer minimizers can be exploited by minimal perfect hashing to substantially improve the space/time trade-off of the dictionary compared to the best-known solutions. AVAILABILITY AND IMPLEMENTATION: https://github.com/jermp/sshash. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Where the Patterns Are: Repetition-Aware Compression for Colored de Bruijn Graphs.

We describe lossless compressed data structures for the colored de Bruijn graph (or c-dBG). Given a collection of reference sequences, a c-dBG can be essentially regarded as a map from k-mers to their color sets. The color set of a k-mer is the set of all identifiers, or colors, of the references that contain the k-mer. While these maps find countless applications in computational biology (e.g., basic query, reading mapping, abundance estimation, etc.), their memory usage represents a serious challenge for large-scale sequence indexing. Our solutions leverage on the intrinsic repetitiveness of the color sets when indexing large collections of related genomes. Hence, the described algorithms factorize the color sets into patterns that repeat across the entire collection and represent these patterns once instead of redundantly replicating their representation as would happen if the sets were encoded as atomic lists of integers. Experimental results across a range of datasets and query workloads show that these representations substantially improve over the space effectiveness of the best previous solutions (sometimes, even dramatically, yielding indexes that are smaller by an order of magnitude). Despite the space reduction, these indexes only moderately impact the efficiency of the queries compared to the fastest indexes.

Where the patterns are: repetition-aware compression for colored de Bruijn graphs ⋆.

We describe lossless compressed data structures for the colored de Bruijn graph (or, c-dBG). Given a collection of reference sequences, a c-dBG can be essentially regarded as a map from k -mers to their color sets . The color set of a k -mer is the set of all identifiers, or colors , of the references that contain the k -mer. While these maps find countless applications in computational biology (e.g., basic query, reading mapping, abundance estimation, etc.), their memory usage represents a serious challenge for large-scale sequence indexing. Our solutions leverage on the intrinsic repetitiveness of the color sets when indexing large collections of related genomes. Hence, the described algorithms factorize the color sets into patterns that repeat across the entire collection and represent these patterns once, instead of redundantly replicating their representation as would happen if the sets were encoded as atomic lists of integers. Experimental results across a range of datasets and query workloads show that these representations substantially improve over the space effectiveness of the best previous solutions (sometimes, even dramatically, yielding indexes that are smaller by an order of magnitude). Despite the space reduction, these indexes only moderately impact the efficiency of the queries compared to the fastest indexes. Software: The implementation of the indexes used for all experiments in this work is written in C++17 and is available at https://github.com/jermp/fulgor .

Fulgor: a fast and compact k-mer index for large-scale matching and color queries.

The problem of sequence identification or matching-determining the subset of reference sequences from a given collection that are likely to contain a short, queried nucleotide sequence-is relevant for many important tasks in Computational Biology, such as metagenomics and pangenome analysis. Due to the complex nature of such analyses and the large scale of the reference collections a resource-efficient solution to this problem is of utmost importance. This poses the threefold challenge of representing the reference collection with a data structure that is efficient to query, has light memory usage, and scales well to large collections. To solve this problem, we describe an efficient colored de Bruijn graph index, arising as the combination of a k-mer dictionary with a compressed inverted index. The proposed index takes full advantage of the fact that unitigs in the colored compacted de Bruijn graph are monochromatic (i.e., all k-mers in a unitig have the same set of references of origin, or color). Specifically, the unitigs are kept in the dictionary in color order, thereby allowing for the encoding of the map from k-mers to their colors in as little as 1 + o(1) bits per unitig. Hence, one color per unitig is stored in the index with almost no space/time overhead. By combining this property with simple but effective compression methods for integer lists, the index achieves very small space. We implement these methods in a tool called Fulgor, and conduct an extensive experimental analysis to demonstrate the improvement of our tool over previous solutions. For example, compared to Themisto-the strongest competitor in terms of index space vs. query time trade-off-Fulgor requires significantly less space (up to 43% less space for a collection of 150,000 Salmonella enterica genomes), is at least twice as fast for color queries, and is 2-6[Formula: see text] faster to construct.

On weighted k-mer dictionaries.

We consider the problem of representing a set of [Formula: see text]-mers and their abundance counts, or weights, in compressed space so that assessing membership and retrieving the weight of a [Formula: see text]-mer is efficient. The representation is called a weighted dictionary of [Formula: see text]-mers and finds application in numerous tasks in Bioinformatics that usually count [Formula: see text]-mers as a pre-processing step. In fact, [Formula: see text]-mer counting tools produce very large outputs that may result in a severe bottleneck for subsequent processing. In this work we extend the recently introduced SSHash dictionary (Pibiri in Bioinformatics 38:185-194, 2022) to also store compactly the weights of the [Formula: see text]-mers. From a technical perspective, we exploit the order of the [Formula: see text]-mers represented in SSHash to encode runs of weights, hence allowing much better compression than the empirical entropy of the weights. We study the problem of reducing the number of runs in the weights to improve compression even further and give an optimal algorithm for this problem. Lastly, we corroborate our findings with experiments on real-world datasets and comparison with competitive alternatives. Up to date, SSHash is the only [Formula: see text]-mer dictionary that is exact, weighted, associative, fast, and small.

Meta-colored compacted de Bruijn graphs.

MOTIVATION: The colored compacted de Bruijn graph (c-dBG) has become a fundamental tool used across several areas of genomics and pangenomics. For example, it has been widely adopted by methods that perform read mapping or alignment, abundance estimation, and subsequent downstream analyses. These applications essentially regard the c-dBG as a map from k-mers to the set of references in which they appear. The c-dBG data structure should retrieve this set -- the color of the k-mer -- efficiently for any given k-mer, while using little memory. To aid retrieval, the colors are stored explicitly in the data structure and take considerable space for large reference collections, even when compressed. Reducing the space of the colors is therefore of utmost importance for large-scale sequence indexing. RESULTS: We describe the meta-colored compacted de Bruijn graph (Mac-dBG) -- a new colored de Bruijn graph data structure where colors are represented holistically, i.e., taking into account their redundancy across the whole collection being indexed, rather than individually as atomic integer lists. This allows the factorization and compression of common sub-patterns across colors. While optimizing the space of our data structure is NP-hard, we propose a simple heuristic algorithm that yields practically good solutions. Results show that the Mac-dBG data structure improves substantially over the best previous space/time trade-off, by providing remarkably better compression effectiveness for the same (or better) query efficiency. This improved space/time trade-off is robust across different datasets and query workloads. Code availability: A C++17 implementation of the Mac-dBG is publicly available on GitHub at: https://github.com/jermp/fulgor.

Fulgor: A fast and compact k-mer index for large-scale matching and color queries.

The problem of sequence identification or matching - determining the subset of references from a given collection that are likely to contain a query nucleotide sequence - is relevant for many important tasks in Computational Biology, such as metagenomics and pan-genome analysis. Due to the complex nature of such analyses and the large scale of the reference collections a resourceefficient solution to this problem is of utmost importance. The reference collection should therefore be pre-processed into an index for fast queries. This poses the threefold challenge of designing an index that is efficient to query, has light memory usage, and scales well to large collections. To solve this problem, we describe how recent advancements in associative, order-preserving, k-mer dictionaries can be combined with a compressed inverted index to implement a fast and compact colored de Bruijn graph data structure. This index takes full advantage of the fact that unitigs in the colored de Bruijn graph are monochromatic (all k-mers in a unitig have the same set of references of origin, or "color"), leveraging the order-preserving property of its dictionary. In fact, k-mers are kept in unitig order by the dictionary, thereby allowing for the encoding of the map from k-mers to their inverted lists in as little as 1+o(1) bits per unitig. Hence, one inverted list per unitig is stored in the index with almost no space/time overhead. By combining this property with simple but effective compression methods for inverted lists, the index achieves very small space. We implement these methods in a tool called Fulgor. Compared to Themisto, the prior state of the art, Fulgor indexes a heterogeneous collection of 30,691 bacterial genomes in 3.8× less space, a collection of 150,000 Salmonella enterica genomes in approximately 2× less space, is at least twice as fast for color queries, and is 2 - 6× faster to construct.