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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…

Data Structures and Algorithms · Computer Science 2026-04-28 Nathaniel K. Brown , Ben Langmead

The Burrows-Wheeler Transform (BWT) moves characters with similar contexts in a text together, where a character's context consists of the characters immediately following it. We say that a property has contextual locality if characters…

Data Structures and Algorithms · Computer Science 2024-11-26 Travis Gagie

The suffix tree is arguably the most fundamental data structure on strings: introduced by Weiner (SWAT 1973) and McCreight (JACM 1976), it allows solving a myriad of computational problems on strings in linear time. Motivated by its large…

Data Structures and Algorithms · Computer Science 2026-05-07 Ruben Becker , Davide Cenzato , Travis Gagie , Sung-Hwan Kim , Ragnar Groot Koerkamp , Giovanni Manzini , Nicola Prezza

We present an algorithm for building the extended BWT (eBWT) of a string collection from its grammar-compressed representation. Our technique exploits the string repetitions captured by the grammar to boost the computation of the eBWT.…

Genomics · Quantitative Biology 2021-02-10 Diego Diaz-Dominguez annd Gonzalo Navarro

We show how to build several data structures of central importance to string processing, taking as input the Burrows-Wheeler transform (BWT) and using small extra working space. Let $n$ be the text length and $\sigma$ be the alphabet size.…

Data Structures and Algorithms · Computer Science 2019-08-14 Nicola Prezza , Giovanna Rosone

Indexing very large collections of strings, such as those produced by the widespread next generation sequencing technologies, heavily relies on multistring generalization of the Burrows-Wheeler Transform (BWT): large requirements of…

Data Structures and Algorithms · Computer Science 2020-12-07 Paola Bonizzoni , Gianluca Della Vedova , Yuri Pirola , Marco Previtali , Raffaella Rizzi

Highly-repetitive collections of strings are increasingly being amassed by genome sequencing and genetic variation experiments, as well as by storing all versions of human-generated files, like webpages and source code. Existing indexes for…

Data Structures and Algorithms · Computer Science 2016-04-22 Djamal Belazzougui , Fabio Cunial , Travis Gagie , Nicola Prezza , Mathieu Raffinot

In this paper we show how to use one or more assembled or partially assembled genome as the basis for a compressed full-text index of its readset. Specifically, we build a labelled tree by taking the assembled genome as a trunk and grafting…

Data Structures and Algorithms · Computer Science 2021-06-02 Travis Gagie , Garance Gourdel , Giovanni Manzini

Given a string $T$ on an alphabet of size $\sigma$, we describe a bidirectional Burrows-Wheeler index that takes $O(|T|\log{\sigma})$ bits of space, and that supports the addition \emph{and removal} of one character, on the left or right…

Data Structures and Algorithms · Computer Science 2019-06-11 Fabio Cunial , Djamal Belazzougui

Some recent results have introduced external-memory algorithms to compute self-indexes of a set of strings, mainly via computing the Burrows-Wheeler Transform (BWT) of the input strings. The motivations for those results stem from…

Data Structures and Algorithms · Computer Science 2015-06-12 Paola Bonizzoni , Gianluca Della Vedova , Yuri Pirola , Marco Previtali , Raffaella Rizzi

The notion of Wheeler languages is rooted in the Burrows-Wheeler transform (BWT), one of the most central concepts in data compression and indexing. The BWT has been generalized to finite automata, the so-called Wheeler automata, by Gagie…

Formal Languages and Automata Theory · Computer Science 2025-04-29 Ruben Becker , Giuseppa Castiglione , Giovanna D'Agostino , Alberto Policriti , Nicola Prezza , Antonio Restivo , Brian Riccardi

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…

Data Structures and Algorithms · Computer Science 2022-07-15 Nathaniel K. Brown , Travis Gagie , Massimiliano Rossi

With the rapid growing of data and number of applications, there is a crucial need of dictionary based reversible transformation techniques to increase the efficiency of the compression algorithms and hence contribute towards the…

Information Theory · Computer Science 2014-03-20 R. R. Baruah , V. Deka , M. P. Bhuyan

Prior work inspired by compression algorithms has described how the Burrows Wheeler Transform can be used to create a distance measure for bioinformatics problems. We describe issues with this approach that were not widely known, and…

Cryptography and Security · Computer Science 2020-02-19 Edward Raff , Charles Nicholas , Mark McLean

We study the impact that string reversal can have on several repetitiveness measures. First, we exhibit an infinite family of strings where the number, $r$, of runs in the run-length encoding of the Burrows--Wheeler transform (BWT) can…

Data Structures and Algorithms · Computer Science 2026-02-17 Hideo Bannai , Yuto Fujie , Peaker Guo , Shunsuke Inenaga , Yuto Nakashima , Simon J. Puglisi , Cristian Urbina

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…

Data Structures and Algorithms · Computer Science 2017-02-07 Alberto Policriti , Nicola Prezza

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…

Data Structures and Algorithms · Computer Science 2026-05-26 Travis Gagie

Indexing highly repetitive texts --- such as genomic databases, software repositories and versioned text collections --- has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive…

Data Structures and Algorithms · Computer Science 2017-07-13 Travis Gagie , Gonzalo Navarro , Nicola Prezza

Indexing highly repetitive texts - such as genomic databases, software repositories and versioned text collections - has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts…

Data Structures and Algorithms · Computer Science 2020-12-17 Travis Gagie , Gonzalo Navarro , Nicola Prezza

A wavelet forest for a text $T [1..n]$ over an alphabet $\sigma$ takes $n H_0 (T) + o (n \log \sigma)$ bits of space and supports access and rank on $T$ in $O (\log \sigma)$ time. K\"arkk\"ainen and Puglisi (2011) implicitly introduced…

Data Structures and Algorithms · Computer Science 2023-08-16 Christina Boucher , Travis Gagie , Aaron Hong , Yansong Li , Norbert Zeh