Faster Maximal Exact Matches with Lazy LCP Evaluation.

MONI (Rossi et al., JCB 2022) is a BWT-based compressed index for computing the matching statistics and maximal exact matches (MEMs) of a pattern (usually a DNA read) with respect to a highly repetitive text (usually a database of genomes) using two operations: LF-steps and longest common extension (LCE) queries on a grammar-compressed representation of the text. In practice, most of the operations are constant-time LF-steps but most of the time is spent evaluating LCE queries. In this paper we show how (a variant of) the latter can be evaluated lazily, so as to bound the total time MONI needs to process the pattern in terms of the number of MEMs between the pattern and the text, while maintaining logarithmic latency.

How to Find Long Maximal Exact Matches and Ignore Short Ones.

Finding maximal exact matches (MEMs) between strings is an important task in bioinformatics, but it is becoming increasingly challenging as geneticists switch to pangenomic references. Fortunately, we are usually interested only in the relatively few MEMs that are longer than we would expect by chance. In this paper we show that under reasonable assumptions we can find all MEMs of length at least L between a pattern of length m and a text of length n in O ( m ) time plus extra O ( l o g n ) time only for each MEM of length at least nearly L using a compact index for the text, suitable for pangenomics.

Taxonomic classification with maximal exact matches in KATKA kernels and minimizer digests.

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 classifiers such as Kraken use k -mers, recent research indicates that using maximal exact matches (MEMs) can lead to better classifications. For example, we can ■ build an augmented FM-index over the the genomes in the tree concatenated in left-to-right order; ■ for each MEM in a read, find the interval in the suffix array containing the starting positions of that MEM's occurrences in those genomes; ■ find the minimum and maximum values stored in that interval; ■ take the lowest common ancestor (LCA) of the genomes containing the characters at those positions. This solution is practical, however, only when the total size of the genomes in the tree is fairly small. In this paper we consider applying the same solution to three lossily compressed representations of the genomes' concatenation: ■ a KATKA kernel, which discards characters that are not in the first or last occurrence of any k max -tuple, for a parameter k max ; a minimizer digest; ■ a KATKA kernel of a minimizer digest. With a test dataset and these three representations of it, simulated reads and various parameter settings, we checked how many reads' longest MEMs occurred only in the sequences from which those reads were generated ("true positive" reads). For some parameter settings we achieved significant compression while only slightly decreasing the true-positive rate.

Maximum-scoring path sets on pangenome graphs of constant treewidth.

We generalize a problem of finding maximum-scoring segment sets, previously studied by Csurös (IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2004, 1, 139-150), from sequences to graphs. Namely, given a vertex-weighted graph G and a non-negative startup penalty c, we can find a set of vertex-disjoint paths in G with maximum total score when each path's score is its vertices' total weight minus c. We call this new problem maximum-scoring path sets (MSPS). We present an algorithm that has a linear-time complexity for graphs with a constant treewidth. Generalization from sequences to graphs allows the algorithm to be used on pangenome graphs representing several related genomes and can be seen as a common abstraction for several biological problems on pangenomes, including searching for CpG islands, ChIP-seq data analysis, analysis of region enrichment for functional elements, or simple chaining problems.

b-move: faster bidirectional character extensions in a run-length compressed index.

Due to the increasing availability of high-quality genome sequences, pan-genomes are gradually replacing single consensus reference genomes in many bioinformatics pipelines to better capture genetic diversity. Traditional bioinformatics tools using the FM-index face memory limitations with such large genome collections. Recent advancements in run-length compressed indices like Gagie et al.'s r-index and Nishimoto and Tabei's move structure, alleviate memory constraints but focus primarily on backward search for MEM-finding. Arakawa et al.'s br-index initiates complete approximate pattern matching using bidirectional search in run-length compressed space, but with significant computational overhead due to complex memory access patterns. We introduce b-move, a novel bidirectional extension of the move structure, enabling fast, cache-efficient bidirectional character extensions in run-length compressed space. It achieves bidirectional character extensions up to 8 times faster than the br-index, closing the performance gap with FM-index-based alternatives, while maintaining the br-index's favorable memory characteristics. For example, all available complete E. coli genomes on NCBI's RefSeq collection can be compiled into a b-move index that fits into the RAM of a typical laptop. Thus, b-move proves practical and scalable for pan-genome indexing and querying. We provide a C++ implementation of b-move, supporting efficient lossless approximate pattern matching including locate functionality, available at https://github.com/biointec/b-move under the AGPL-3.0 license.

Pfp-fm: an accelerated FM-index.

FM-indexes are crucial data structures in DNA alignment, but searching with them usually takes at least one random access per character in the query pattern. Ferragina and Fischer [1] observed in 2007 that word-based indexes often use fewer random accesses than character-based indexes, and thus support faster searches. Since DNA lacks natural word-boundaries, however, it is necessary to parse it somehow before applying word-based FM-indexing. In 2022, Deng et al. [2] proposed parsing genomic data by induced suffix sorting, and showed that the resulting word-based FM-indexes support faster counting queries than standard FM-indexes when patterns are a few thousand characters or longer. In this paper we show that using prefix-free parsing-which takes parameters that let us tune the average length of the phrases-instead of induced suffix sorting, gives a significant speedup for patterns of only a few hundred characters. We implement our method and demonstrate it is between 3 and 18 times faster than competing methods on queries to GRCh38, and is consistently faster on queries made to 25,000, 50,000 and 100,000 SARS-CoV-2 genomes. Hence, it seems our method accelerates the performance of count over all state-of-the-art methods with a moderate increase in the memory. The source code for PFP - FM is available at https://github.com/AaronHong1024/afm .

Movi: a fast and cache-efficient full-text pangenome index.

Efficient pangenome indexes are promising tools for many applications, including rapid classification of nanopore sequencing reads. Recently, a compressed-index data structure called the "move structure" was proposed as an alternative to other BWT-based indexes like the FM index and r-index. The move structure uniquely achieves both O(r) space and O(1)-time queries, where r is the number of runs in the pangenome BWT. We implemented Movi, an efficient tool for building and querying move-structure pangenome indexes. While the size of the Movi's index is larger than the r-index, it scales at a smaller rate for pangenome references, as its size is exactly proportional to r, the number of runs in the BWT of the reference. Movi can compute sophisticated matching queries needed for classification - such as pseudo-matching lengths and backward search - at least ten times faster than the fastest available methods, and in some cases more than 30-fold faster. Movi achieves this speed by leveraging the move structure's strong locality of reference, incurring close to the minimum possible number of cache misses for queries against large pangenomes. We achieve still further speed improvements by using memory prefetching to attain a degree of latency hiding that would be difficult with other index structures like the r-index. Movi's fast constant-time query loop makes it well suited to real-time applications like adaptive sampling for nanopore sequencing, where decisions must be made in a small and predictable time interval.

PFP-FM: An Accelerated FM-index.

FM-indexes are a crucial data structure in DNA alignment, but searching with them usually takes at least one random access per character in the query pattern. Ferragina and Fischer [1] observed in 2007 that word-based indexes often use fewer random accesses than character-based indexes, and thus support faster searches. Since DNA lacks natural word-boundaries, however, it is necessary to parse it somehow before applying word-based FM-indexing. Last year, Deng et al. [2] proposed parsing genomic data by induced suffix sorting, and showed the resulting word-based FM-indexes support faster counting queries than standard FM-indexes when patterns are a few thousand characters or longer. In this paper we show that using prefix-free parsing-which takes parameters that let us tune the average length of the phrases-instead of induced suffix sorting, gives a significant speedup for patterns of only a few hundred characters. We implement our method and demonstrate it is between 3 and 18 times faster than competing methods on queries to GRCh38, and is consistently faster on queries made to 25,000, 50,000 and 100,000 SARS-CoV-2 genomes. Hence, it seems our method accelerates the performance of count over all state-of-the-art methods with a minor increase in the memory. The source code for PFP-FM is available at https://github.com/marco-oliva/afm.

µ- PBWT: a lightweight r-indexing of the PBWT for storing and querying UK Biobank data.

MOTIVATION: The Positional Burrows-Wheeler Transform (PBWT) is a data structure that indexes haplotype sequences in a manner that enables finding maximal haplotype matches in h sequences containing w variation sites in O(hw) time. This represents a significant improvement over classical quadratic-time approaches. However, the original PBWT data structure does not allow for queries over Biobank panels that consist of several millions of haplotypes, if an index of the haplotypes must be kept entirely in memory. RESULTS: In this article, we leverage the notion of r-index proposed for the BWT to present a memory-efficient method for constructing and storing the run-length encoded PBWT, and computing set maximal matches (SMEMs) queries in haplotype sequences. We implement our method, which we refer to as µ-PBWT, and evaluate it on datasets of 1000 Genome Project and UK Biobank data. Our experiments demonstrate that the µ-PBWT reduces the memory usage up to a factor of 20% compared to the best current PBWT-based indexing. In particular, µ-PBWT produces an index that stores high-coverage whole genome sequencing data of chromosome 20 in about a third of the space of its BCF file. µ-PBWT is an adaptation of techniques for the run-length compressed BWT for the PBWT (RLPBWT) and it is based on keeping in memory only a succinct representation of the RLPBWT that still allows the efficient computation of set maximal matches (SMEMs) over the original panel. AVAILABILITY AND IMPLEMENTATION: Our implementation is open source and available at https://github.com/dlcgold/muPBWT. The binary is available at https://bioconda.github.io/recipes/mupbwt/README.html.

SPUMONI 2: improved classification using a pangenome index of minimizer digests.

Genomics analyses use large reference sequence collections, like pangenomes or taxonomic databases. SPUMONI 2 is an efficient tool for sequence classification of both short and long reads. It performs multi-class classification using a novel sampled document array. By incorporating minimizers, SPUMONI 2's index is 65 times smaller than minimap2's for a mock community pangenome. SPUMONI 2 achieves a speed improvement of 3-fold compared to SPUMONI and 15-fold compared to minimap2. We show SPUMONI 2 achieves an advantageous mix of accuracy and efficiency in practical scenarios such as adaptive sampling, contamination detection and multi-class metagenomics classification.

Recursive Prefix-Free Parsing for Building Big BWTs.

Prefix-free parsing is useful for a wide variety of purposes including building the BWT, constructing the suffix array, and supporting compressed suffix tree operations. This linear-time algorithm uses a rolling hash to break an input string into substrings, where the resulting set of unique substrings has the property that none of the substrings' suffixes (of more than a certain length) is a proper prefix of any of the other substrings' suffixes. Hence, the name prefix-free parsing. This set of unique substrings is referred to as the dictionary . The parse is the ordered list of dictionary strings that defines the input string. Prior empirical results demonstrated the size of the parse is more burdensome than the size of the dictionary for large, repetitive inputs. Hence, the question arises as to how the size of the parse can scale satisfactorily with the input. Here, we describe our algorithm, recursive prefix-free parsing , which accomplishes this by computing the prefix-free parse of the parse produced by prefix-free parsing an input string. Although conceptually simple, building the BWT from the parse-of-the-parse and the dictionaries is significantly more challenging. We solve and implement this problem. Our experimental results show that recursive prefix-free parsing is extremely effective in reducing the memory needed to build the run-length encoded BWT of the input. Our implementation is open source and available at https://github.com/marco-oliva/r-pfbwt .

Recursive Prefix-Free Parsing for Building Big BWTs.

Prefix-free parsing is useful for a wide variety of purposes including building the BWT, constructing the suffix array, and supporting compressed suffix tree operations. This linear-time algorithm uses a rolling hash to break an input string into substrings, where the resulting set of unique substrings has the property that none of the substrings' suffixes (of more than a certain length) is a proper prefix of any of the other substrings' suffixes. Hence, the name prefix-free parsing. This set of unique substrings is referred to as the dictionary. The parse is the ordered list of dictionary strings that defines the input string. Prior empirical results demonstrated the size of the parse is more burdensome than the size of the dictionary for large, repetitive inputs. Hence, the question arises as to how the size of the parse can scale satisfactorily with the input. Here, we describe our algorithm, recursive prefix-free parsing, which accomplishes this by computing the prefix-free parse of the parse produced by prefix-free parsing an input string. Although conceptually simple, building the BWT from the parse-of-the-parse and the dictionaries is significantly more challenging. We solve and implement this problem. Our experimental results show that recursive prefix-free parsing is extremely effective in reducing the memory needed to build the run-length encoded BWT of the input. Our implementation is open source and available at https://github.com/marco-oliva/r-pfbwt.

Space-time Trade-offs for the LCP Array of Wheeler DFAs.

Recently, Conte et al. generalized the longest-common prefix (LCP) array from strings to Wheeler DFAs, and they showed that it can be used to efficiently determine matching statistics on a Wheeler DFA [DCC 2023]. However, storing the LCP array requires O n log n bits, n being the number of states, while the compact representation of Wheeler DFAs often requires much less space. In particular, the BOSS representation of a de Bruijn graph only requires a linear number of bits, if the size of alphabet is constant. In this paper, we propose a sampling technique that allows to access an entry of the LCP array in logarithmic time by only storing a linear number of bits. We use our technique to provide a space-time tradeoff to compute matching statistics on a Wheeler DFA. In addition, we show that by augmenting the BOSS representation of a k -th order de Bruijn graph with a linear number of bits we can navigate the underlying variable-order de Bruijn graph in time logarithmic in k , thus improving a previous bound by Boucher et al. which was linear in k [DCC 2015].

Computing matching statistics on Wheeler DFAs.

Matching statistics were introduced to solve the approximate string matching problem, which is a recurrent subroutine in bioinformatics applications. In 2010, Ohlebusch et al. [SPIRE 2010] proposed a time and space efficient algorithm for computing matching statistics which relies on some components of a compressed suffix tree - notably, the longest common prefix (LCP) array. In this paper, we show how their algorithm can be generalized from strings to Wheeler deterministic finite automata. Most importantly, we introduce a notion of LCP array for Wheeler automata, thus establishing a first clear step towards extending (compressed) suffix tree functionalities to labeled graphs.

Augmented Thresholds for MONI.

MONI (Rossi et al., 2022) can store a pangenomic dataset T in small space and later, given a pattern P, quickly find the maximal exact matches (MEMs) of P with respect to T. In this paper we consider its one-pass version (Boucher et al., 2021), whose query times are dominated in our experiments by longest common extension (LCE) queries. We show how a small modification lets us avoid most of these queries which significantly speeds up MONI in practice while only slightly increasing its size.

Data Structures for SMEM-Finding in the PBWT.

The positional Burrows-Wheeler Transform (PBWT) was presented as a means to find set-maximal exact matches (SMEMs) in haplotype data via the computation of the divergence array. Although run-length encoding the PBWT has been previously considered, storing the divergence array along with the PBWT in a compressed manner has not been as rigorously studied. We define two queries that can be used in combination to compute SMEMs, allowing us to define smaller data structures that support one or both of these queries. We combine these data structures, enabling the PBWT and the divergence array to be stored in a manner that allows for finding SMEMs. We estimate and compare the memory usage of these data structures, leading to one data structure that is most memory efficient. Lastly, we implement this data structure and compare its performance to prior methods using various datasets taken from the 1000 Genomes Project data.

Syotti: scalable bait design for DNA enrichment.

MOTIVATION: Bait enrichment is a protocol that is becoming increasingly ubiquitous as it has been shown to successfully amplify regions of interest in metagenomic samples. In this method, a set of synthetic probes ('baits') are designed, manufactured and applied to fragmented metagenomic DNA. The probes bind to the fragmented DNA and any unbound DNA is rinsed away, leaving the bound fragments to be amplified for sequencing. Metsky et al. demonstrated that bait-enrichment is capable of detecting a large number of human viral pathogens within metagenomic samples. RESULTS: We formalize the problem of designing baits by defining the Minimum Bait Cover problem, show that the problem is NP-hard even under very restrictive assumptions, and design an efficient heuristic that takes advantage of succinct data structures. We refer to our method as Syotti. The running time of Syotti shows linear scaling in practice, running at least an order of magnitude faster than state-of-the-art methods, including the method of Metsky et al. At the same time, our method produces bait sets that are smaller than the ones produced by the competing methods, while also leaving fewer positions uncovered. Lastly, we show that Syotti requires only 25 min to design baits for a dataset comprised of 3 billion nucleotides from 1000 related bacterial substrains, whereas the method of Metsky et al. shows clearly super-linear running time and fails to process even a subset of 17% of the data in 72 h. AVAILABILITY AND IMPLEMENTATION: https://github.com/jnalanko/syotti. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MONI: A Pangenomic Index for Finding Maximal Exact Matches.

Recently, Gagie et al. proposed a version of the FM-index, called the r-index, that can store thousands of human genomes on a commodity computer. Then Kuhnle et al. showed how to build the r-index efficiently via a technique called prefix-free parsing (PFP) and demonstrated its effectiveness for exact pattern matching. Exact pattern matching can be leveraged to support approximate pattern matching, but the r-index itself cannot support efficiently popular and important queries such as finding maximal exact matches (MEMs). To address this shortcoming, Bannai et al. introduced the concept of thresholds, and showed that storing them together with the r-index enables efficient MEM finding-but they did not say how to find those thresholds. We present a novel algorithm that applies PFP to build the r-index and find the thresholds simultaneously and in linear time and space with respect to the size of the prefix-free parse. Our implementation called MONI can rapidly find MEMs between reads and large-sequence collections of highly repetitive sequences. Compared with other read aligners-PuffAligner, Bowtie2, BWA-MEM, and CHIC- MONI used 2-11 times less memory and was 2-32 times faster for index construction. Moreover, MONI was less than one thousandth the size of competing indexes for large collections of human chromosomes. Thus, MONI represents a major advance in our ability to perform MEM finding against very large collections of related references.

Finding Maximal Exact Matches Using the r-Index.

Efficiently finding maximal exact matches (MEMs) between a sequence read and a database of genomes is a key first step in read alignment. But until recently, it was unknown how to build a data structure in [Formula: see text] space that supports efficient MEM finding, where r is the number of runs in the Burrows-Wheeler Transform. In 2021, Rossi et al. showed how to build a small auxiliary data structure called thresholds in addition to the r-index in [Formula: see text] space. This addition enables efficient MEM finding using the r-index. In this article, we present the tool that implements this solution, which we call MONI. Namely, we give a high-level view of the main components of the data structure and show how the source code can be downloaded, compiled, and used to find MEMs between a set of sequence reads and a set of genomes.

RLBWT Tricks.

Until recently, most experts would probably have agreed we cannot backwards-step in constant time with a run-length compressed Burrows-Wheeler Transform (RLBWT), since doing so relies on rank queries on sparse bitvectors and those inherit lower bounds from predecessor queries. At ICALP '21, however, Nishimoto and Tabei described a new, simple and constant-time implementation. For a permutation π , it stores an O r -space table - where r is the number of positions i where either i = 0 or π i + 1 ≠ π i + 1 - that enables the computation of successive values of π i by table look-ups and linear scans. Nishimoto and Tabei showed how to increase the number of rows in the table to bound the length of the linear scans such that the query time for computing π i is constant while maintaining O r -space. In this paper we refine Nishimoto and Tabei's approach, including a time-space tradeoff, and experimentally evaluate different implementations demonstrating the practicality of part of their result. We show that even without adding rows to the table, in practice we almost always scan only a few entries during queries. We propose a decomposition scheme of the permutation π corresponding to the LF-mapping that allows an improved compression of the data structure, while limiting the query time. We tested our implementation on real-world genomic datasets and found that without compression of the table, backward-stepping is drastically faster than with sparse bitvector implementations but, unfortunately, also uses drastically more space. After compression, backward-stepping is competitive both in time and space with the best existing implementations.