Abstract
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 Lyndonlike 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). Here we apply these subcomputations, along with Θ(n) suffix-sorting (Ko and Aluru, 2003), 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). Motivation for this work arises in possible applications to data compression.
Original language | English |
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Pages (from-to) | 77-89 |
Number of pages | 13 |
Journal | Theoretical Computer Science |
Volume | 531 |
Early online date | 12 Mar 2014 |
DOIs | |
Publication status | Published - 24 Apr 2014 |
Externally published | Yes |
Keywords
- algorithm
- bijective
- Burrows-Wheeler Transform
- complexity
- lexicographic order
- lex-extension order
- linear
- lyndon word
- string
- suffix array
- total order
- V-BWT
- V- order
- V -transform
- V -word
- word