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

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.