A bijective variant of the Burrows-Wheeler Transform using V-order

J.W. Daykin, William Smyth

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    © 2014 Elsevier B.V. In this paper we introduce the V-transform (V-BWT), a variant of the classic Burrows-Wheeler Transform. The original BWT uses lexicographic order, whereas we apply a distinct total ordering of strings called V-order. V-order string comparison and Lyndon-like factorization of a string x=. x[1. ..n] into V-words have recently been shown to be linear in their use of time and space (Daykin et al., 2011) [18]. Here we apply these subcomputations, along with Θ(n) suffix-sorting (Ko and Aluru, 2003) [26], to implement linear V-sorting of all the rotations of a string. When it is known that the input string x is a V-word, we compute the V-transform in Θ(n) time and space, and also outline an efficient algorithm for inverting the V-transform and recovering x. We further outline a bijective algorithm in the case that x is arbitrary. We propose future research into other variants of transforms using lex-extension orderings (Daykin et al., 2013) [19]. Motivation for this work arises in possible applications to data compression.
    Original languageEnglish
    Pages (from-to)77-89
    JournalTheoretical Computer Science
    Volume531
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Burrows-Wheeler Transform
    Bijective
    Strings
    Mathematical transformations
    Transform
    Sorting
    Total ordering
    Data compression
    Lexicographic Order
    Factorization
    Suffix
    Data Compression
    Efficient Algorithms
    Distinct
    Arbitrary

    Cite this

    Daykin, J.W. ; Smyth, William. / A bijective variant of the Burrows-Wheeler Transform using V-order. In: Theoretical Computer Science. 2014 ; Vol. 531. pp. 77-89.
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    abstract = "{\circledC} 2014 Elsevier B.V. In this paper we introduce the V-transform (V-BWT), a variant of the classic Burrows-Wheeler Transform. The original BWT uses lexicographic order, whereas we apply a distinct total ordering of strings called V-order. V-order string comparison and Lyndon-like factorization of a string x=. x[1. ..n] into V-words have recently been shown to be linear in their use of time and space (Daykin et al., 2011) [18]. Here we apply these subcomputations, along with Θ(n) suffix-sorting (Ko and Aluru, 2003) [26], to implement linear V-sorting of all the rotations of a string. When it is known that the input string x is a V-word, we compute the V-transform in Θ(n) time and space, and also outline an efficient algorithm for inverting the V-transform and recovering x. We further outline a bijective algorithm in the case that x is arbitrary. We propose future research into other variants of transforms using lex-extension orderings (Daykin et al., 2013) [19]. Motivation for this work arises in possible applications to data compression.",
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    A bijective variant of the Burrows-Wheeler Transform using V-order. / Daykin, J.W.; Smyth, William.

    In: Theoretical Computer Science, Vol. 531, 2014, p. 77-89.

    Research output: Contribution to journalArticle

    TY - JOUR

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    AB - © 2014 Elsevier B.V. In this paper we introduce the V-transform (V-BWT), a variant of the classic Burrows-Wheeler Transform. The original BWT uses lexicographic order, whereas we apply a distinct total ordering of strings called V-order. V-order string comparison and Lyndon-like factorization of a string x=. x[1. ..n] into V-words have recently been shown to be linear in their use of time and space (Daykin et al., 2011) [18]. Here we apply these subcomputations, along with Θ(n) suffix-sorting (Ko and Aluru, 2003) [26], to implement linear V-sorting of all the rotations of a string. When it is known that the input string x is a V-word, we compute the V-transform in Θ(n) time and space, and also outline an efficient algorithm for inverting the V-transform and recovering x. We further outline a bijective algorithm in the case that x is arbitrary. We propose future research into other variants of transforms using lex-extension orderings (Daykin et al., 2013) [19]. Motivation for this work arises in possible applications to data compression.

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