IA Scholar Query: Fast Label Extraction in the CDAWG
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 23 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Indexing Highly Repetitive String Collections
https://scholar.archive.org/work/irqubq5jingijnqaansju762bi
Two decades ago, a breakthrough in indexing string collections made it possible to represent them within their compressed space while at the same time offering indexed search functionalities. As this new technology permeated through applications like bioinformatics, the string collections experienced a growth that outperforms Moore's Law and challenges our ability of handling them even in compressed form. It turns out, fortunately, that many of these rapidly growing string collections are highly repetitive, so that their information content is orders of magnitude lower than their plain size. The statistical compression methods used for classical collections, however, are blind to this repetitiveness, and therefore a new set of techniques has been developed in order to properly exploit it. The resulting indexes form a new generation of data structures able to handle the huge repetitive string collections that we are facing. In this survey we cover the algorithmic developments that have led to these data structures. We describe the distinct compression paradigms that have been used to exploit repetitiveness, the fundamental algorithmic ideas that form the base of all the existing indexes, and the various structures that have been proposed, comparing them both in theoretical and practical aspects. We conclude with the current challenges in this fascinating field.Gonzalo Navarrowork_irqubq5jingijnqaansju762biWed, 23 Nov 2022 00:00:00 GMTSensitivity of string compressors and repetitiveness measures
https://scholar.archive.org/work/rdfeynbyqvcgtbrdkke3grr2g4
The sensitivity of a string compression algorithm C asks how much the output size C(T) for an input string T can increase when a single character edit operation is performed on T. We analyze the worst-case multiplicative sensitivity of string compression algorithms, which is defined by max_T ∈Σ^n{C(T')/C(T) : ed(T, T') = 1}, where ed(T, T') denotes the edit distance between T and T'. In particular, for the most common versions of the Lempel-Ziv 77 compressors, we prove that the worst-case multiplicative sensitivity is only a small constant. We strengthen our upper bound results by presenting matching lower bounds. We also generalize these results to the smallest bidirectional scheme b. These results contrast with the previously known related results such that the size z_ 78 of the Lempel-Ziv 78 factorization can increase by a factor of Ω(n^1/4) [Lagarde and Perifel, 2018], and the number r of runs in the Burrows-Wheeler transform can increase by a factor of Ω(log n) [Giuliani et al., 2021] when a character is prepended to an input string of length n. In addition, we show that the worst-case multiplicative sensitivity of r is upper bounded by O(log r log n). We also study the worst-case sensitivity of several grammar-based compressors including RePair, LongestMatch, Bisection, AVL-grammar, GCIS, and CDAWG. Further, we extend the notion of the worst-case sensitivity to string repetitiveness measures such as the smallest string attractor size γ and the substring complexity δ. We present some non-trivial upper and lower bounds of the worst-case multiplicative sensitivity for γ and matching upper and lower bounds of the worst-case multiplicative sensitivity for δ. We also exhibit the worst-case additive sensitivity max_T ∈Σ^n{C(T') - C(T) : ed(T, T') = 1}.Tooru Akagi, Mitsuru Funakoshi, Shunsuke Inenagawork_rdfeynbyqvcgtbrdkke3grr2g4Sun, 06 Nov 2022 00:00:00 GMTResolution of the burrows-wheeler transform conjecture
https://scholar.archive.org/work/zax7fvx56nh35bomurgmaflwui
The Burrows-Wheeler Transform (BWT) is an invertible text transformation that permutes symbols of a text according to the lexicographical order of its suffixes. BWT is the main component of popular lossless compression programs (such as bzip2) as well as recent powerful compressed indexes (such as the r-index 7 ), central in modern bioinformatics. The compressibility of BWT is quantified by the number r of equal-letter runs in the output. Despite the practical significance of BWT, no nontrivial upper bound on r is known. By contrast, the sizes of nearly all other known compression methods have been shown to be either always within a polylog n factor (where n is the length of the text) from z, the size of Lempel-Ziv (LZ77) parsing of the text, or much larger in the worst case (by an n e factor for e > 0). In this paper, we show that r = O (z log 2 n) holds for every text. This result has numerous implications for text indexing and data compression; in particular: (1) it proves that many results related to BWT automatically apply to methods based on LZ77, for example, it is possible to obtain functionality of the suffix tree in O (z polylog n) space; (2) it shows that many text processing tasks can be solved in the optimal time assuming the text is compressible using LZ77 by a sufficiently large polylog n factor; and (3) it implies the first nontrivial relation between the number of runs in the BWT of the text and of its reverse. In addition, we provide an O (z polylog n)-time algorithm converting the LZ77 parsing into the run-length compressed BWT. To achieve this, we develop several new data structures and techniques of independent interest. In particular, we define compressed string synchronizing sets (generalizing the recently introduced powerful technique of string synchronizing sets 11 ) and show how to efficiently construct them. Next, we propose a new variant of wavelet trees for sequences of long strings, establish a nontrivial bound on their size, and describe efficient construction algorithms. Finally, we develop new indexes that can be constructed directly from the LZ77 parsing and efficiently support pattern matching queries on text substrings.Dominik Kempa, Tomasz Kociumakawork_zax7fvx56nh35bomurgmaflwui