Abstract
Original language | English |
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Pages (from-to) | 77-89 |
Journal | Theoretical Computer Science |
Volume | 531 |
DOIs | |
Publication status | Published - 2014 |
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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 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 -