Burrows–Wheeler transform and LCP array construction in constant space

Louza, Felipe A.; Gagie, Travis; Telles, Guilherme P.

doi:10.1016/j.jda.2016.11.003

Cited by 13 publications

(13 citation statements)

References 44 publications

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“…Finally, Crochemore et al [23] showed how to transform a text into its Burrows-Wheeler transform by using O(lg n) of additional bits. Due to da Louza et al [24], this algorithm was extended to compute simultaneously the longest common prefix (LCP) array [21] with O(lg n) bits of additional working space.…”

Section: Related Workmentioning

confidence: 99%

Re-Pair in Small Space

et al. 2020

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Re-Pairis a grammar compression scheme with favorably good compression rates. The computation of Re-Pair comes with the cost of maintaining large frequency tables, which makes it hard to compute Re-Pair on large-scale data sets. As a solution for this problem, we present, given a text of length n whose characters are drawn from an integer alphabet with size σ=nO(1), an O(min(n2,n2lglogτnlglglgn/logτn)) time algorithm computing Re-Pair with max((n/c)lgn,nlgτ)+O(lgn) bits of working space including the text space, where c≥1 is a fixed user-defined constant and τ is the sum of σ and the number of non-terminals. We give variants of our solution working in parallel or in the external memory model. Unfortunately, the algorithm seems not practical since a preliminary version already needs roughly one hour for computing Re-Pair on one megabyte of text.

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Section: Related Workmentioning

confidence: 99%

Re-Pair in Small Space

et al. 2020

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“…The BWT has been subject of intense research in the last two decades, from compression [11,16,17,29], algorithmic [9,24,30], and combinatorial [10,13,32] points of view (mentioning just a tiny selection from the recent literature). It has also been extended in several ways.…”

Section: Related Workmentioning

confidence: 99%

When a Dollar Makes a BWT

Giuliani,

Lipták,

Masillo

et al. 2019

Preprint

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The Burrows-Wheeler-Transform (BWT) is a reversible string transformation which plays a central role in text compression and is fundamental in many modern bioinformatics applications. The BWT is a permutation of the characters, which is in general better compressible and allows to answer several different query types more efficiently than the original string. It is easy to see that not every string is a BWT image, and exact characterizations of BWT images are known. We investigate a related combinatorial question. In many applications, a sentinel character $ is added to mark the end of the string, and thus the BWT of a string ending with $ contains exactly one $ character. We ask, given a string w, in which positions, if any, can the $-character be inserted to turn w into the BWT image of a word ending with the sentinel character. We show that this depends only on the standard permutation of w and give a combinatorial characterization of such positions via this permutation. We then develop an O(n log n)-time algorithm for identifying all such positions, improving on the naive quadratic time algorithm.

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“…We presented an algorithm that computes the BWT in-place together with the LCP array in quadratic time using constant workspace [Louza and Telles 2015]. We also introduced the first algorithm to compute the LCP array directly in a compressed representation [Louza et al 2017a].…”

Section: Bwt and Lcp Construction In Constant Spacementioning

confidence: 99%

Engineering Augmented Suffix Sorting Algorithms

Louza¹,

Telles²,

Gog³

2018

Anais Do Concurso De Teses E Dissertações Da SBC (CTD-SBC)

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Strings are prevalent in Computer Science and algorithms for their efficient processing are fundamental in various applications. The results introduced in this work contribute with theoretical improvements and practical advances in building full-text indexes. Our first contribution is an in-place algorithm that computes the Burrows-Wheeler transform and the longest common prefix (LCP) array. Our second contribution is the construction of the suffix array augmented with the LCP array in optimal time and space for strings from constant size alphabets. Our third contribution is a set of algorithms to construct full-text indexes for string collections in optimal theoretical bounds. This work is an extended abstract of the Ph.D. thesis of the first author.

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Burrows–Wheeler transform and LCP array construction in constant space

Cited by 13 publications

References 44 publications

Re-Pair in Small Space

Re-Pair in Small Space

When a Dollar Makes a BWT

Engineering Augmented Suffix Sorting Algorithms

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