The k-spectrum of a string is the set of all distinct substrings of length k occurring in the string. This is a lossy but computationally convenient representation of the information in the string, with many applications in high-throughput bioinformatics. In this work, we define the notion of the Spectral Burrows-Wheeler Transform (SBWT), which is a sequence of subsets of the alphabet of the string encoding the k-spectrum of the string. The SBWT is a distillation of the ideas found in the BOSS and Wheeler graph data structures. We explore multiple different approaches to index the SBWT for membership queries on the underlying k-spectrum. We identify subset rank queries as the essential subproblem, and propose four succinct index structures to solve it. One of the approaches essentially leads to the known BOSS data structure, while the other three offer attractive time-space trade-offs and support simpler query algorithms that rely only on fast rank queries. The most general approach involves a novel data structure we dub the subset wavelet tree, which we find to be of independent interest. All of the approaches are also amendable to entropy compression, which leads to good space bounds on the sizes of the data structures. Using entropy compression, we show that the SBWT can support membership queries on the k-spectrum of a single string in O(k) time and (n + k)(log σ + 1/ln 2) + o((n + k)σ) bits of space, where n is the number of distinct substrings of length k in the input and σ is the size of the alphabet. This improves from the time O(k log σ) achieved by the BOSS data structure, while maintaining the same asymptotic space complexity of O(n log σ), albeit with smaller constant factors. We show, via experiments on a range of genomic data sets, that the simplicity of our new indexes translates into large performance gains in practice over prior art.

Motivation: Huge data sets containing whole-genome sequences of bacterial strains are now commonplace and represent a rich and important resource for modern genomic epidemiology and metagenomics. In order to efficiently make use of these data sets, efficient indexing data structures - that are both scalable and provide rapid query throughput - are paramount. Results: Here, we present Themisto, a scalable colored k-mer index designed for large collections of microbial reference genomes, that works for both short and long read data. Themisto indexes 179 thousand Salmonella enterica genomes in 9 hours. The resulting index takes 142 gigabytes, and Themisto pseudoaligns reads from a Salmonella enterica isolate sample against the index at a rate of 2 million base pairs per second on 48 threads. In comparison, the best competing tools Metagraph and Bifrost were only able to index 11 thousand genomes in the same time. In pseudoalignment, these other tools were either an order of magnitude slower than Themisto, or used an order of magnitude more memory. Themisto also offers superior pseudoalignment quality, achieving a higher recall than previous methods on Nanopore read sets. Availability and implementation: Themisto is available and documented as a C++ package at https://github.com/algbio/themisto available under the GPLv2 license.

Motivation Huge datasets containing whole-genome sequences of bacterial strains are now commonplace and represent a rich and important resource for modern genomic epidemiology and metagenomics. In order to efficiently make use of these datasets, efficient indexing data structures—that are both scalable and provide rapid query throughput—are paramount. Results Here, we present Themisto, a scalable colored k-mer index designed for large collections of microbial reference genomes, that works for both short and long read data. Themisto indexes 179 thousand Salmonella enterica genomes in 9 h. The resulting index takes 142 gigabytes. In comparison, the best competing tools Metagraph and Bifrost were only able to index 11 000 genomes in the same time. In pseudoalignment, these other tools were either an order of magnitude slower than Themisto, or used an order of magnitude more memory. Themisto also offers superior pseudoalignment quality, achieving a higher recall than previous methods on Nanopore read sets. Availability and implementation Themisto is available and documented as a C++ package at https://github.com/algbio/themisto available under the GPLv2 license.