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Nathaniel K. Brown

Publications and source records attributed to Nathaniel K. Brown.

8 recordsLinked to original sources
arXiv2026

Optimal-Time Move Structure Construction

The move structure represents a permutation $π$ of $[0,n)$ by partitioning the domain into $O(r)$ disjoint, contiguously permuted intervals, with $r$ being the minimum number of such intervals. This data structure occupies $O(r)$ words of space and enables $O(1)$-time computation of $π(i)$ given the interval that contains $i$. For permutations where $r \ll n$, this provides an efficient, compressed representation for navigation. While existing best $O(r)$-space construction approaches require $O(r\log r)$-time, we present an optimal $O(r)$-time and space construction algorithm. This is achieved by replacing balanced search trees with pointer-based lists by introducing a bidirectional strategy that synchronizes construction of the structures for $π$ and its inverse $π^{-1}$ in a single, unified pass. By applying this algorithm, we achieve the first optimal $O(n)$-time construction of the longest common prefix (LCP) array from a run-length-encoded Burrows-Wheeler transform (RLBWT) of $r$ runs in $O(r)$ working space. Empirical evaluation on pangenome-scale data confirms that our move structure construction algorithm is consistently faster than the previous best, achieving speedups of up to $\sim 2\times$ with comparable memory usage.

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arXiv2026

Bounding the Average Move Structure Query for Faster and Smaller RLBWT Permutations

The move structure represents permutations with long contiguously permuted intervals in compressed space with optimal query time. They have become an important feature of compressed text indexes using space proportional to the number of Burrows-Wheeler Transform (BWT) runs, often applied in genomics. This is in thanks not only to theoretical improvements over past approaches, but great cache efficiency and average case query time in practice. This is true even without using the worst case guarantees provided by the interval splitting balancing of the original result. In this paper, we show that an even simpler type of splitting, length capping by truncating long intervals, bounds the average move structure query time to optimal whilst obtaining a superior construction time than the traditional approach. This also proves constant query time when amortized over a full traversal of a single cycle permutation from an arbitrary starting position. Such a scheme has surprising benefits both in theory and practice. For a move structure with $r$ runs over a domain $n$, we replace all $O(r \log n)$-bit components to reduce the overall representation by $O(r \log r)$-bits. The worst case query time is also improved to $O(\log \frac{n}{r})$ without balancing. An $O(r)$-time and $O(r)$-space construction lets us apply the method to run-length encoded BWT (RLBWT) permutations such as LF and $ϕ$ to obtain optimal-time algorithms for BWT inversion and suffix array (SA) enumeration in $O(r)$ additional working space. Finally, we introduce the Orbit library for move structure support, and use it to evaluate our splitting approach. Experiments find length capping construction is faster and uses less memory than balancing, with faster queries. We also see a space reduction in practice, with at least a $\sim 40\%$ disk size decrease for LF across large repetitive genomic collections.

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arXiv2025

KeBaB: $k$-mer based breaking for finding long MEMs

Long maximal exact matches (MEMs) are used in many genomics applications such as read classification and sequence alignment. Li's ropebwt3 finds long MEMs quickly because it can often ignore much of its input. In this paper we show that a fast and space efficient $k$-mer filtration step using a Bloom filter speeds up MEM-finders such as ropebwt3 even further by letting them ignore even more. We also show experimentally that our approach can accelerate metagenomic classification without significantly hurting accuracy.

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arXiv2025

Faster run-length compressed suffix arrays

We first review how we can store a run-length compressed suffix array (RLCSA) for a text $T$ of length $n$ over an alphabet of size $σ$ whose Burrows-Wheeler Transform (BWT) consists of $r$ runs in $O \left( \rule{0ex}{2ex} r \log (n / r) + r \log σ+ σ\right)$ bits such that later, given character $a$ and the suffix array interval for $P$, we can find the suffix-array (SA) interval for $a P$ in $O (\log r_a + \log \log n)$ time, where $r_a$ is the number of runs of copies of $a$ in the BWT. We then show how to modify the RLCSA such that we find the SA interval for $a P$ in only $O (\log r_a)$ time, without increasing its asymptotic space bound. Our key idea is applying a result by Nishimoto and Tabei (ICALP 2021) and then replacing rank queries on sparse bitvectors by a constant number of select queries. We also review two-level indexing and discuss how our faster RLCSA may be useful in improving it. Finally, we briefly discuss how two-level indexing may speed up a recent heuristic for finding maximal exact matches of a pattern with respect to an indexed text.

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arXiv2023

Faster Maximal Exact Matches with Lazy LCP Evaluation

MONI (Rossi et al., {\it 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.

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arXiv2022

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 and thus significantly speeds up MONI in practice while only slightly increasing its size.

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arXiv2022

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 $π(i + 1) \neq π(i) + 1$ -- 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.

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