### Abstract

Original language | English |
---|---|

Pages (from-to) | 77-89 |

Journal | Theoretical Computer Science |

Volume | 531 |

DOIs | |

Publication status | Published - 2014 |

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### Cite this

*Theoretical Computer Science*,

*531*, 77-89. https://doi.org/10.1016/j.tcs.2014.03.014

}

*Theoretical Computer Science*, vol. 531, pp. 77-89. https://doi.org/10.1016/j.tcs.2014.03.014

**A bijective variant of the Burrows-Wheeler Transform using V-order.** / Daykin, J.W.; Smyth, William.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A bijective variant of the Burrows-Wheeler Transform using V-order

AU - Daykin, J.W.

AU - Smyth, William

PY - 2014

Y1 - 2014

N2 - © 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.

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.

U2 - 10.1016/j.tcs.2014.03.014

DO - 10.1016/j.tcs.2014.03.014

M3 - Article

VL - 531

SP - 77

EP - 89

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -