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 .

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.

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.

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].