Lempel-Ziv Factorization Revisited

Ohlebusch, Enno; Gog, Simon

doi:10.1007/978-3-642-21458-5_4

Cited by 51 publications

(44 citation statements)

References 15 publications

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“…We implemented in C++ the online LZ77 parsing algorithm of Theorem 6 (the source code is available at [22]). There are lots of work for LZ77 parsing (e.g., see [31][32][33][34][35][36][37][38][39][40][41][42][43] and references therein). Among them we choose the ones whose implementations potentially work in the peak RAM usage smaller than n lg σ + n lg n bits and compare with our method.…”

Section: Resultsmentioning

confidence: 99%

Refining the r-index

Bannai

Gagie

Tomohiro

2020

Theoretical Computer Science

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Section: Resultsmentioning

confidence: 99%

Refining the r-index

Bannai

Gagie

Tomohiro

2020

Theoretical Computer Science

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“…Thus, for a LZ76 implementation with linear time and space complexities, a data structure allowing the back referencing of any LZ76 string pattern l i in Oðjl i jÞ time is required. Suitable data structures for this purpose are a suffix tree [34], or a combination of a suffix array and a longest common prefix (LCP) array [35], [36], [37], [38], [39]. Computation of the LZ76 complexity measure with either data structure is straightforward, as it requires a single OðnÞ parsing pass over the input [41].…”

Section: Related Workmentioning

confidence: 99%

FLOTT—A Fast, Low Memory T-TransformAlgorithm for Measuring String Complexity

Rebenich

Speidel

Neville

et al. 2014

IEEE Trans. Comput.

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This paper presents flott, a fast, low memory T-transform algorithm which can be used to compute the string complexity measure T-complexity. The algorithm uses approximately one third of the memory of its predecessor while reducing the running time by about 20 percent. The flott implementation has the same worst-case memory requirements as state of the art suffix tree construction algorithms. A suffix tree can be used to efficiently compute the Lempel-Ziv production complexity, which is another measure of string complexity. The C-implementation of flott is available as Open Source software.

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“…1 More recently, LZ factorization has been studied by various authors [36][37][38][39][40], with consequent improvement in efficiency and practicality. For our purposes, there are two pertinent facts:…”

Section: Preliminariesmentioning

confidence: 99%

Large-scale detection of repetitions

Smyth

2014

Phil. Trans. R. Soc. A.

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Combinatorics on words began more than a century ago with a demonstration that an infinitely long string with no repetitions could be constructed on an alphabet of only three letters. Computing all the repetitions (such as ⋯ TTT ⋯ or ⋯ CGACGA ⋯ ) in a given string x of length n is one of the oldest and most important problems of computational stringology, requiring time in the worst case. About a dozen years ago, it was discovered that repetitions can be computed as a by-product of the Θ ( n )-time computation of all the maximal periodicities or runs in x . However, even though the computation is linear, it is also brute force: global data structures, such as the suffix array , the longest common prefix array and the Lempel–Ziv factorization , need to be computed in a preprocessing phase. Furthermore, all of this effort is required despite the fact that the expected number of runs in a string is generally a small fraction of the string length. In this paper, I explore the possibility that repetitions (perhaps also other regularities in strings) can be computed in a manner commensurate with the size of the output.

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Lempel-Ziv Factorization Revisited

Cited by 51 publications

References 15 publications

Refining the r-index

Refining the r-index

FLOTT—A Fast, Low Memory T-TransformAlgorithm for Measuring String Complexity

Large-scale detection of repetitions

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