Efficient Algorithms for the Inverse Sort Transform

Nong, Ge; Zhang, Sen

doi:10.1109/tc.2007.70762

Cited by 11 publications

(10 citation statements)

References 24 publications

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“…We observe a quite similar situation [5], [6] in the Sort Transform (ST) [7], which has been proposed as a finite-order variant of the BWT. The ST, which is also a special case of the GRP transform, was originally developed to speed up the BWT.…”

Section: Introductionmentioning

confidence: 60%

“…Similarly, we can consider the case where we limit the order d to an integer k < n with = 1. This is known as the k-order variant of the BWT, or sometimes called the Sort Transform (ST) [5], [6], [7]. Now, consider an application of the ST to a string over A .…”

Section: Relation With Existing Transformsmentioning

confidence: 99%

“…The inverse transformation above is based on the framework of Nong and Zhang [5]. A key issue in the framework lies in the computation of D, which they called the context switch vector.…”

Section: Computation Of Vector Dmentioning

confidence: 99%

“…This aim was achieved in its forward transformation with a trade-off of a more demanding and complicated inverse transformation. Nong and Zhang [5] have addressed the problem of developing an efficient inverse ST transform, and gave a linear time/space algorithm with Chan in their recent paper [6].…”

Section: Introductionmentioning

confidence: 99%

“…Our main emphasis is on the development of an efficient inverse transformation. For this, we apply the technique by Nong, Zhang, and Chan [5], [6] to our transform. Its details and other remarks on complexity issues will be given separately in Section 3.…”

Section: Introductionmentioning

confidence: 99%

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Extension and Faster Implementation of the GRP Transform for Lossless Compression

Yokoo

2010

Combinatorial Pattern Matching

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Abstract. The GRP transform, or the generalized radix permutation transform was proposed as a parametric generalization of the BWT of the block-sorting data compression algorithm. This paper develops its extension that can be applied with any combination of parameters. By using the technique developed for linear time/space implementation of the sort transform, we propose an efficient implementation for the inverse transformation of the GRP transform. It works for arbitrary parameter values, and can convert the transformed string to the original string in time linear in the string length.

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Section: Introductionmentioning

confidence: 60%

Section: Relation With Existing Transformsmentioning

confidence: 99%

“…The inverse transformation above is based on the framework of Nong and Zhang [5]. A key issue in the framework lies in the computation of D, which they called the context switch vector.…”

Section: Computation Of Vector Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Extension and Faster Implementation of the GRP Transform for Lossless Compression

Yokoo

2010

Combinatorial Pattern Matching

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Revisiting bounded context block‐sorting transformations

2011

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The Burrows-Wheeler Transform (BWT) produces a permutation of a string X, denoted X , by sorting the n cyclic rotations of X into full lexicographical order and taking the last column of the resulting n n matrix to be X . The transformation is reversible in O.n/ time. In this paper, we consider an alteration to the process, called k-BWT, where rotations are only sorted to a depth k. We propose new approaches to the forward and reverse transform, and show that the methods are efficient in practice. More than a decade ago, two algorithms were independently discovered for reversing k-BWT, both of which run in O.nk/ time. Two recent algorithms have lowered the bounds for the reverse transformation to O.n log k/ and O.n/, respectively. We examine the practical performance for these reversal algorithms. We find that the original O.nk/ approach is most efficient in practice, and investigates new approaches, aimed at further speeding reversal, which store precomputed context boundaries in the compressed file. By explicitly encoding the context boundaries, we present an O.n/ reversal technique that is both efficient and effective. Finally, our study elucidates an inherently cache-friendly -and hitherto unobserved -behavior in the reverse k-BWT, which could lead to new applications of the k-BWT transform. In contrast to previous empirical studies, we show that the partial transform can be reversed significantly faster than the full transform, without significantly affecting compression effectiveness. approach in which the n rotations are only partially sorted to a fixed prefix depth, k. We refer to this modified transform as k-BWT. By limiting the sort depth to k, sorting can be accomplished in O.nk/ time using radix sort and is very fast in practice. Moreover, Schindler reports nearly identical compression effectiveness to the full transform, even for small values of k. The algorithms developed by Schindler [13] were subsequently made available in the general purpose compression tool szip. However, the simplification of the forward k-BWT transform comes at a cost: the reverse transform becomes more expensive, at least in theory.Our contribution: First, we describe an efficient forward k-BWT algorithm based on induced sorting techniques from suffix array construction [15]. Our second contribution is a practical, O.n/ k-BWT time reversal algorithm that implicitly stores context boundaries. Third, we provide the first thorough empirical analysis of state-of-the-art k-BWT algorithms for the forward and inverse transforms, compression effectiveness, and associated trade-offs. Lastly, we discover a previously undocumented locality of access property inherent to k-BWT algorithms, allowing fast transform reversal for small k. BACKGROUND AND NOTATIONLet X D XOE0..n D XOE0XOE1..XOEn be a string (or text) of n C 1 symbols, where the first n symbols of X are drawn from an alphabet † and comprise the actual input; XOEn D $ is a unique "endof-string" symbol that is defined to be lexicographically smaller than all symbols in †. The stri...

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Computing Inverse ST in Linear Complexity

Nong

Zhang

Chan

Combinatorial Pattern Matching

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Efficient Algorithms for the Inverse Sort Transform

Cited by 11 publications

References 24 publications

Extension and Faster Implementation of the GRP Transform for Lossless Compression

Extension and Faster Implementation of the GRP Transform for Lossless Compression

Revisiting bounded context block‐sorting transformations

Computing Inverse ST in Linear Complexity

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