An Extension of the Burrows Wheeler Transform and Applications to Sequence Comparison and Data Compression

Mantaci, Sabrina; Restivo, Antonio; Rosone, Giovanna; Sciortino, Marinella

doi:10.1007/11496656_16

Cited by 35 publications

(53 citation statements)

References 10 publications

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“…In this section we recall the definition of an extension of the Burrows-Wheeler transform (called ebwt) to a multiset S of primitive words that, as the original bwt, is defined on conjugates (see [16,17]). The ebwt has been inspired by a remark in [6], where the authors pointed out that the bwt coincides with a particular case of a bijection defined in [10].…”

Section: Generalizations Of Bwt To a Multiset Of Wordsmentioning

confidence: 99%

“…In [16], the authors give an extension of the bwt (called ebwt) to a multiset S of words on the alphabet Σ, suggested by the remark given in [6], that the bwt coincides with a particular case of a bijection defined in [10] by Gessel and Reutenauer. The ebwt of a multiset S is a word obtained by a letters permutation of the words in S induced by the sorting of the conjugates of words in S according with an order relation (denoted by ≺ ω ) defined by using lexicographic order among infinite words.…”

Section: Introductionmentioning

confidence: 98%

“…It is also used as preprocessing of compressors on a single text, where the ebwt is applied to the words obtained by a factorization of the text. For instance, in [16], the input is factorized into blocks of equal length, whereas in [12,14] the Lyndon factorization of the text is used.…”

Section: Introductionmentioning

confidence: 99%

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Sorting Conjugates and Suffixes of Words in a Multiset

Bonomo

Mantaci

Restivo

et al. 2014

Int. J. Found. Comput. Sci.

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Section: Generalizations Of Bwt To a Multiset Of Wordsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Sorting Conjugates and Suffixes of Words in a Multiset

Bonomo

Mantaci

Restivo

et al. 2014

Int. J. Found. Comput. Sci.

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“…Other notable contributions to the BWT research arena include: the BWT is shown to be a special case of the Gessel and Reutenauer transformation [9]; a generalization of the BWT suitable for a multiset of words and applied to the problem of the whole mitochondrial genome phylogeny is given in [31]; slashing the time for the BWT inversion is presented in [21]; and a constant-space comparison-based algorithm for computing the BWT is proposed in [10].…”

Section: The Burrows-wheeler Transformmentioning

confidence: 99%

Indeterminate String Factorizations and Degenerate Text Transformations

Daykin

Watson

2017

Math.Comput.Sci.

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The data explosion problem continues to escalate requiring novel and ingenious solutions. Pattern inference focusing on repetitive structures in data is a vigorous field of endeavor aimed at shrinking volumes of data by means of concise descriptions. The Burrows-Wheeler transformation computes a permutation of a string of letters over an alphabet, and is well-suited to compression-related applications due to its invertability and data clustering properties. For space efficiency the input to the transform can be preprocessed into Lyndon factors. Rather than this classic deterministic approach for letter based strings, we consider scenarios with uncertainty regarding the data: a position in an indeterminate or degenerate string is a set of letters. We first define indeterminate Lyndon words and establish their associated unique string factorization; then we introduce the novel degenerate Burrows-Wheeler transformation which may apply the indeterminate Lyndon factorization. A core computation in Burrows-Wheeler type transforms is the linear sorting of all conjugates of the input string-we achieve this in the degenerate case with lex-extension ordering. Like the original forms, indeterminate Lyndon factorization and the degenerate transform and its inverse can all be computed in linear time and space with respect to total input size of degenerate strings. Regular molecular biological strings yield a wealth of applications of big data-an important motivation for generalizing to degenerate strings is their extensive use in expressing polymorphism in DNA sequences.

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“…Notably the transform has the property that it tends to cluster occurrences of the same letter in the input string into repetitions (runs), and moreover, that it is reversible. Due to this data-clustering property, the Burrows-Wheeler Transform finds wideranging applications in: preprocessing for data compression (it is also called block-sorting compression) and it is core to the bzip2 family of text compressors; bioinformatics and sequence processing [BCRS13,MRRS05]; and text indexing [FM00] -indeed the versatility of the transform is increasing to include, for instance, multimedia information retrieval [ABM08].…”

Section: Introductionmentioning

confidence: 99%

Binary block order Rouen Transform

Daykin¹,

Groult²,

Guesnet³

et al. 2016

Theoretical Computer Science

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Please cite this article in press as: J.W. Daykin et al., Binary block order Rouen transform, Theoret. Comput. Sci. (2016), http://dx.doi.org/10.1016/j.tcs. 2016.05.028 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights• Novel twin binary Burrows-Wheeler type transforms are introduced.• The transforms are defined for Lyndon-like B-words which apply binary block order.• We call this approach the B-BWT Rouen Transform.• These bijective Rouen transforms and inverses are computed in linear time.• Preliminary experimental results indicate potential value of binary transforms. Binary Block Order Rouen Transform

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An Extension of the Burrows Wheeler Transform and Applications to Sequence Comparison and Data Compression

Cited by 35 publications

References 10 publications

Sorting Conjugates and Suffixes of Words in a Multiset

Sorting Conjugates and Suffixes of Words in a Multiset

Indeterminate String Factorizations and Degenerate Text Transformations

Binary block order Rouen Transform

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