Related papers: Bounding the Average Move Structure Query for Fast…
The Burrows-Wheeler Transform (BWT) is a fundamental component in many data structures for text indexing and compression, widely used in areas such as bioinformatics and information retrieval. The extended BWT (eBWT) generalizes the…
The Lempel-Ziv factorization (LZ77) and the Run-Length encoded Burrows-Wheeler Transform (RLBWT) are two important tools in text compression and indexing, being their sizes $z$ and $r$ closely related to the amount of text…
The Burrows-Wheeler Transform (BWT) is an efficient invertible text transformation algorithm with the properties of tending to group identical characters together in a run, and enabling search of the text. This transformation has extensive…
The positional Burrows-Wheeler Transform (PBWT) is commonly used to store haplotype panels compactly in such a way that, given a query haplotype, we can quickly find the set maximal exact matches (SMEMs) between the query and the haplotypes…
Range Minimum Query (RMQ) is an important building brick of many compressed data structures and string matching algorithms. Although this problem is essentially solved in theory, with sophisticated data structures allowing for constant time…
The run-length compressed Burrows-Wheeler transform (RLBWT) used in conjunction with the backward search introduced in the FM index is the centerpiece of most compressed indexes working on highly-repetitive data sets like biological…
Common intervals have been defined as a modelisation of gene clusters in genomes represented either as permutations or as sequences. Whereas optimal algorithms for finding common intervals in permutations exist even for an arbitrary number…
The Burrows Wheeler transform has applications in data compression as well as full text indexing. Despite its important applications and various existing algorithmic approaches the construction of the transform for large data sets is still…
We show how to merge two run-length compressed Burrows-Wheeler Transforms (RLBWTs) into a run-length compressed extended Burrows-Wheeler Transform (eBWT) in $O (r)$ space and $O ((r + L) \log (m + n))$ time, where $m$ and $n$ are the…
The Burrows-Wheeler transform (BWT) is a well studied text transformation widely used in data compression and text indexing. The BWT of two strings can also provide similarity measures between them, based on the observation that the more…
A Longest Common Extension (LCE) query on a text $T$ of length $N$ asks for the length of the longest common prefix of suffixes starting at given two positions. We show that the signature encoding $\mathcal{G}$ of size $w = O(\min(z \log N…
Popular sequence alignment tools such as BWA convert a reference genome to an indexing data structure based on the Burrows-Wheeler Transform (BWT), from which matches to individual query sequences can be rapidly determined. However the…
The $r$-index (Gagie et al., JACM 2020) represented a breakthrough in compressed indexing of repetitive text collections, outperforming its alternatives by orders of magnitude. Its space usage, $\mathcal{O}(r)$ where $r$ is the number of…
A self-index is a compressed data structure that supports locate queries -- reporting all positions where a given pattern occurs in a string while maintaining the string in compressed form. While many self-indexes have been proposed,…
The Burrows-Wheeler Transform is a string transformation that plays a fundamental role for the design of self-indexing compressed data structures. Over the years, researchers have successfully extended this transformation outside the…
Indexing of very large collections of strings such as those produced by the widespread sequencing technologies, heavily relies on multi-string generalizations of the Burrows-Wheeler Transform (BWT), and for this problem various in-memory…
Constructing the Burrows-Wheeler transform (BWT) for long strings poses significant challenges regarding construction time and memory usage. We use a prefix of the suffix array to partition a long string into shorter substrings, thereby…
In highly repetitive strings, like collections of genomes from the same species, distinct measures of repetition all grow sublinearly in the length of the text, and indexes targeted to such strings typically depend only on one of these…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
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 $\sigma$ whose Burrows-Wheeler Transform (BWT) consists of $r$ runs in $O \left( \rule{0ex}{2ex} r \log (n /…