An Approximation Algorithm for Space-optimal Encoding of a Text

Katajainen, Jyrki; Raita, T.

doi:10.1093/comjnl/32.3.228

Cited by 15 publications

(25 citation statements)

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“…How much efficiently (in time and space) we can compute the bit-optimal LZ77-parsing of S? Several solutions are indeed known for this problem but they are either inefficient [30,10], in that they take Θ(n 2 ) worst-case time and space, or they are approximate [20], or they rely on heuristics [22,31,3,6,10] which do not provide any guarantee on the time/space performance of the compression process. This is the reason why Rajpoot and Sahinalp stated in [28, pag.…”

Section: Introductionmentioning

confidence: 99%

On the bit-complexity of Lempel-Ziv compression

Ferragina¹,

Nitto²,

Venturini³

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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One of the most famous and investigated lossless datacompression schemes is the one introduced by Lempel and Ziv about 30 years ago [37]. This compression scheme is known as "dictionary-based compressor" and consists of squeezing an input string by replacing some of its substrings with (shorter) codewords which are actually pointers to a dictionary of phrases built as the string is processed. Surprisingly enough, although many fundamental results are nowadays known about the speed and effectiveness of this compression process (see e.g. [23,28] and references therein), "we are not aware of any parsing scheme that achieves optimality when the LZ77-dictionary is in use under any constraint on the codewords other than being of equal length" [28, pag. 159]. Here optimality means to achieve the minimum number of bits in compressing each individual input string, without any assumption on its generating source. In this paper we investigate three issues pertaining to the bit-complexity of LZ-based compressors, and we design algorithms which achieve bit-optimality in the compressed output size by taking efficient/optimal time and optimal space. These theoretical results will be sustained by some experiments that will compare our novel LZ-based compressors against the most popular compression tools (like gzip, bzip2) and state-of-theart compressors (like the booster of [14,13]).

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Section: Introductionmentioning

confidence: 99%

On the bit-complexity of Lempel-Ziv compression

Ferragina¹,

Nitto²,

Venturini³

2009

Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms

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“…For Elias' codes [10], Fibonacci's codes [11], and most practical integer encoders used for search engines and data compressors [30,36], it is Q(f, n) = Q(g, n) = O(log n). Therefore | G(S)| = O(n log n), so it is smaller than the complete graph built and used by previous papers [31,20,16]. For the encoders used in gzip, it is Q(f, n) = Q(g, n) = O(1) and | G(S)| = O(n).…”

Section: Theoremmentioning

confidence: 97%

“…However, this is Θ(n 2 ) in the worst case (take e.g. S = a n [31,20]) thus resulting inefficient and actually un-usable in practice even for strings of few Megabytes. In what follows we show that the computation of the SSSP can be restricted to a subgraph of G(S) whose size depends on the choice of f and g satisfying Property 1, and is O(n log n) for most known integer-encoding functions.…”

Section: Bit-optimal Parsing and Sssp-problemmentioning

confidence: 99%

“…How much efficiently (in time and space) can we compute the bit-optimal LZ77-parsing of S? Several solutions are indeed known for this problem but they are either inefficient [31,16], in that they take Θ(n 2 ) worst-case time and space, or they are approximate [20], or they rely on heuristics [22,32,4,6,16] which do not provide any guarantee on the time/space performance of the compression process. This is the reason why Rajpoot and Sahinalp stated in [29, pag.…”

Section: Introductionmentioning

confidence: 99%

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Bit-Complexity of Lempel-Ziv Compression

Venturini

2013

Atlantis Studies in Computing

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One of the most famous and investigated lossless data-compression schemes is the one introduced by Lempel and Ziv about 30 years ago [37]. This compression scheme is known as "dictionary-based compressor" and consists of squeezing an input string by replacing some of its substrings with (shorter) codewords which are actually pointers to a dictionary of phrases built as the string is processed. Surprisingly enough, although many fundamental results are nowadays known about the speed and effectiveness of this compression process (see e.g. [23,29] and references therein), "we are not aware of any parsing scheme that achieves optimality when the LZ77-dictionary is in use under any constraint on the codewords other than being of equal length" [29, pag. 159]. Here optimality means to achieve the minimum number of bits in compressing each individual input string, without any assumption on its generating source. In this paper we investigate three issues pertaining to the bit-complexity of LZ-based compressors, and we design algorithms which achieve bit-optimality in the compressed output size by taking efficient/optimal time and optimal space. These theoretical results will be sustained by some experiments that will compare our novel LZ-based compressors against the most popular compression tools (like gzip, bzip2) and state-of-the-art compressors (like the booster of [13,12]).

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“…By using an algorithm for finding the shortest path in a network, Katajainen and Raita (1989) gave a procedure that, given a phrase book, obtains a time-efficient approximation algorithm for the space-optimal encoding.…”

Section: Introductionmentioning

confidence: 99%

Improving semistatic compression via phrase-based modeling

Brisaboa

Fariña

Navarro

et al. 2011

Information Processing & Management

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In this work we go one step beyond by using phrases as source symbols. We present two new semistatic modelers that we combined with a dense coding scheme to obtain two new compressors: Pair-Based End-Tagged Dense Code (PETDC), where source symbols can be either words or pairs of words, and Phrase-Based End-Tagged Dense Code (PhETDC), which considers words and sequences of words (phrases). PETDC compresses English texts to 28-29% and PhETDC to around 23%, outperforming the optimal byteoriented zero-order prefix-free word-based semistatic compressor by up to 8 percentage points. Moreover, PETDC and PhETDC still permit random access and efficient direct searches using fast Boyer-Moore algorithms.

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An Approximation Algorithm for Space-optimal Encoding of a Text

Cited by 15 publications

References 0 publications

On the bit-complexity of Lempel-Ziv compression

On the bit-complexity of Lempel-Ziv compression

Bit-Complexity of Lempel-Ziv Compression

Improving semistatic compression via phrase-based modeling

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