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.
|Number of pages||13|
|Journal||Theoretical Computer Science|
|Early online date||12 Mar 2014|
|Publication status||Published - 24 Apr 2014|
- Burrows-Wheeler Transform
- lexicographic order
- lex-extension order
- lyndon word
- suffix array
- total order
- V- order
- V -transform
- V -word
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- Faculty of Business and Physcial Sciences, Department of Computer Science - Honorary Research Fellow