73 research outputs found
On Bijective Variants of the Burrows-Wheeler Transform
The sort transform (ST) is a modification of the Burrows-Wheeler transform
(BWT). Both transformations map an arbitrary word of length n to a pair
consisting of a word of length n and an index between 1 and n. The BWT sorts
all rotation conjugates of the input word, whereas the ST of order k only uses
the first k letters for sorting all such conjugates. If two conjugates start
with the same prefix of length k, then the indices of the rotations are used
for tie-breaking. Both transforms output the sequence of the last letters of
the sorted list and the index of the input within the sorted list. In this
paper, we discuss a bijective variant of the BWT (due to Scott), proving its
correctness and relations to other results due to Gessel and Reutenauer (1993)
and Crochemore, Desarmenien, and Perrin (2005). Further, we present a novel
bijective variant of the ST.Comment: 15 pages, presented at the Prague Stringology Conference 2009 (PSC
2009
String Comparison in -Order: New Lexicographic Properties & On-line Applications
-order is a global order on strings related to Unique Maximal
Factorization Families (UMFFs), which are themselves generalizations of Lyndon
words. -order has recently been proposed as an alternative to
lexicographical order in the computation of suffix arrays and in the
suffix-sorting induced by the Burrows-Wheeler transform. Efficient -ordering
of strings thus becomes a matter of considerable interest. In this paper we
present new and surprising results on -order in strings, then go on to
explore the algorithmic consequences
Constructing the bijective and the extended burrows-wheeler transform in linear time
Publisher Copyright: © Hideo Bannai, Juha Kärkkäinen, Dominik Köppl, and Marcin Piatkowski.The Burrows-Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT (BBWT) is a bijective variant of it. Although it is known that the BWT can be constructed in linear time for integer alphabets by using a linear time suffix array construction algorithm, it was up to now only conjectured that the BBWT can also be constructed in linear time. We confirm this conjecture in the word RAM model by proposing a construction algorithm that is based on SAIS, improving the best known result of O(n lg n/ lg lg n) time to linear. Since we can reduce the problem of constructing the extended BWT to constructing the BBWT in linear time, we obtain a linear-time algorithm computing the extended BWT at the same time.Peer reviewe
A new class of string transformations for compressed text indexing
Introduced about thirty years ago in the field of data compression, the Burrows-Wheeler Transform (BWT) is a string transformation that, besides being a booster of the performance of memoryless compressors, plays a fundamental role in the design of efficient self-indexing compressed data structures. Finding other string transformations with the same remarkable properties of BWT has been a challenge for many researchers for a long time. In this paper, we introduce a whole class of new string transformations, called local orderings-based transformations, which have all the “myriad virtues” of BWT. As a further result, we show that such new string transformations can be used for the construction of the recently introduced r-index, which makes them suitable also for highly repetitive collections. In this context, we consider the problem of finding, for a given string, the BWT variant that minimizes the number of runs in the transformed string
Constructing the Bijective and the Extended Burrows-Wheeler Transform in Linear Time
The Burrows-Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The bijective BWT (BBWT) is a bijective variant of it. Although it is known that the BWT can be constructed in linear time for integer alphabets by using a linear time suffix array construction algorithm, it was up to now only conjectured that the BBWT can also be constructed in linear time. We confirm this conjecture in the word RAM model by proposing a construction algorithm that is based on SAIS, improving the best known result of O(n lg n / lg lg n) time to linear. Since we can reduce the problem of constructing the extended BWT to constructing the BBWT in linear time, we obtain a linear-time algorithm computing the extended BWT at the same time
In-Place Bijective Burrows-Wheeler Transforms
One of the most well-known variants of the Burrows-Wheeler transform (BWT) [Burrows and Wheeler, 1994] is the bijective BWT (BBWT) [Gil and Scott, arXiv 2012], which applies the extended BWT (EBWT) [Mantaci et al., TCS 2007] to the multiset of Lyndon factors of a given text. Since the EBWT is invertible, the BBWT is a bijective transform in the sense that the inverse image of the EBWT restores this multiset of Lyndon factors such that the original text can be obtained by sorting these factors in non-increasing order.
In this paper, we present algorithms constructing or inverting the BBWT in-place using quadratic time. We also present conversions from the BBWT to the BWT, or vice versa, either (a) in-place using quadratic time, or (b) in the run-length compressed setting using ?(n lg r / lg lg r) time with ?(r lg n) bits of words, where r is the sum of character runs in the BWT and the BBWT
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