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Lempel-Ziv-like Parsing in Small Space [article]

Dmitry Kosolobov, Daniel Valenzuela, Gonzalo Navarro, Simon J. Puglisi
2020 arXiv   pre-print
Lempel-Ziv (LZ77 or, briefly, LZ) is one of the most effective and widely-used compressors for repetitive texts.  ...  An alternative is Relative Lempel-Ziv (RLZ), which indexes only a fixed reference sequence, whose size can be controlled.  ...  Lempel-Ziv Parsers In this section we compare the performance and scalability of ReLZ against other Lempel-Ziv parsers that can also run in small memory (this time, using Approximation ratioẑ/z for different  ... 
arXiv:1903.01909v2 fatcat:4ewm5bjl7zbdxfmdtc76zcxkqa

Lempel–Ziv-Like Parsing in Small Space

Dmitry Kosolobov, Daniel Valenzuela, Gonzalo Navarro, Simon J. Puglisi
2020 Algorithmica  
Lempel-Ziv (LZ77 or, briefly, LZ) is one of the most effective and widely-used compressors for repetitive texts.  ...  An alternative is Relative Lempel-Ziv (RLZ), which indexes only a fixed reference sequence, whose size can be controlled.  ...  Lempel-Ziv Parsers In this section we compare the performance and scalability of ReLZ against other Lempel-Ziv parsers that can also run in small memory (this time, using EMLZ [21] : External-memory  ... 
doi:10.1007/s00453-020-00722-6 fatcat:goav33vs5ne7jhubr737q6zogi

Data Compression Support in Databases

Balakrishna R. Iyer, David Wilhite
1994 Very Large Data Bases Conference  
Roughly speaking, a slight increase in cpu cycles is more than offset by savings in I/O subsystem.  ...  in the overall computer system architecture, unit of compression, update in place, and the application of log' to compressed data.  ...  Figure 3 : Building a Ziv-Lempel parse tree In building the parse tree, Ziv and Lempel [ZL77, ZL78] permit the tree to grow without bound while Welch [We841 and Miller and Wegman [MW85] refer to approaches  ... 
dblp:conf/vldb/IyerW94 fatcat:5atidjxm4rdazgodd4zlbk4rci

On the average redundancy rate of the Lempel-Ziv code

G. Louchard, W. Szpankowski
1997 IEEE Transactions on Information Theory  
, Lempel-Ziv parsing scheme, generalized Lempel-Ziv scheme, average redundancy rate, digital search trees, suffix trees.  ...  This result is a consequence ofrecently established second-order properties for the number of phrases in the Lempel-Ziv algorithm.  ...  ACKNOWLEDGEMENT We would like to thank M. Feder, P. Jacquet, J. Kieffer and P. Shields for helpful comments and discussions regarding this work.  ... 
doi:10.1109/18.567640 fatcat:hg7iozitwzhedow2dgn2hcmthm

Approximating Optimal Bidirectional Macro Schemes [article]

Luís M. S. Russo, Ana D. Correia, Gonzalo Navarro, Alexandre P. Francisco
2020 arXiv   pre-print
Lempel-Ziv is an easy-to-compute member of a wide family of so-called macro schemes; it restricts pointers to go in one direction only.  ...  We test our algorithm on a number of artificial repetitive texts and verify that it is efficient in practice and outperforms Lempel-Ziv, sometimes by a wide margin.  ...  A simple solution is to initialize our algorithm with a Lempel-Ziv parsing.  ... 
arXiv:2003.02336v1 fatcat:ecfjurml2vbxzondih5ilmhbji

On the Approximation Ratio of Lempel-Ziv Parsing [chapter]

Travis Gagie, Gonzalo Navarro, Nicola Prezza
2018 Lecture Notes in Computer Science  
Since computing b is NP-complete, a popular gold standard is z, the number of phrases in the Lempel-Ziv parse of the text, where phrases can be copied only from the left.  ...  A plausible lower bound is b, the least number of phrases of a general bidirectional parse of a text, where phrases can be copied from anywhere else in the text.  ...  Lempel-Ziv Parsing Lempel and Ziv [23] define a parsing of T into the fewest possible phrases T = Z 1 . . . Z z , so that each phrase Z i is a substring (but not a suffix) of Z 1 . . .  ... 
doi:10.1007/978-3-319-77404-6_36 fatcat:lqhuqs3ohbht5dsx3wtorpmgdy

Pushdown Compression

Pilar Albert, Elvira Mayordomo, Philip Moser, Sylvain Perifel, Marc Herbstritt
2008 Symposium on Theoretical Aspects of Computer Science  
We prove that Lempel-Ziv is incomparable with pushdown compressors.  ...  pushdown compressors that allows a formal analysis of their performance and a more ambitious use of the stack in XML compression, where so far it is mainly connected to parsing mechanisms.  ...  In section 4 we show that there is a sequence on which Lempel-Ziv outperforms pushdown compressors and in section 5 we show that Lempel-Ziv and pushdown compression are incomparable.  ... 
doi:10.4230/lipics.stacs.2008.1332 dblp:conf/stacs/AlbertMMP08 fatcat:ipybgu6r5nbatjnbwrhbodb7pa

A Lempel-Ziv like approach for signal classification

Jugurta Montalvão, Jânio Canuto
2014 TEMA  
In this paper, the seminal method proposed by Abraham Lempel and Jacob Ziv, aimed at the complexity analysis of sequences of symbols, was modified to compare similarities between two sequences.  ...  Moreover, as compared to a conventional pattern recognition method, the new approach provided better performances in terms of Equal Error Ratio in speaker verification experiments.  ...  The Modified Lempel-Ziv (MLZ) parsing procedure starts by searching for y p 1 1 (initially p 1 = 1) inside x m 1 .  ... 
doi:10.5540/tema.2014.015.02.0223 fatcat:ijnltnxfcjb7dbca3o3fwt5ql4

Polylog Space Compression Is Incomparable with Lempel-Ziv and Pushdown Compression [chapter]

Elvira Mayordomo, Philippe Moser
2009 Lecture Notes in Computer Science  
We study the performance attained by these algorithms and show they are incomparable with both pushdown compressors and the Lempel-Ziv compression algorithm.  ...  This paper considers online compression algorithms that use at most polylogarithmic space (plogon). These algorithms correspond to compressors in the data stream model.  ...  The comparison of pushdown and Lempel Ziv has been presented in [2] .  ... 
doi:10.1007/978-3-540-95891-8_56 fatcat:o5jbvscdq5gk5d7l2n27wf6l7y

Indexing Highly Repetitive String Collections [article]

Gonzalo Navarro
2022 arXiv   pre-print
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  ...  Space complexities are measured in amount of computer words, that is, O(X) space means O(X log n) bits. By poly x we mean any polynomial in x, that is, x O(1) , and polylog x denotes poly (log x).  ... 
arXiv:2004.02781v9 fatcat:rceyc6ti5jdfpebkrbbgq3kine

Average Profile of the Generalized Digital Search Tree and the Generalized Lempel--Ziv Algorithm

Guy Louchard, Wojciech Szpankowski, Jing Tang
1998 SIAM journal on computing (Print)  
In the generalized Lempel-Ziv parsing scheme, one partitions a sequence of symbols from a finite alphabet into phrases such that the new phrase is the shortest substring seen in the past by at most b-l  ...  In this paper, we investigate the depth of a randomly selected node in such a tree and the length of a randomly selected phrase in the generalized Lempel-Ziv scheme.  ...  related to the length of a randomly selected phrase in the generalized Lempel-Ziv parsing scheme.  ... 
doi:10.1137/s0097539796301811 fatcat:krqbkmgweban3ezvlphaui3i7i

On the Approximation Ratio of Ordered Parsings [article]

Gonzalo Navarro, Carlos Ochoa, Nicola Prezza
2019 arXiv   pre-print
Since computing b is NP-complete, a popular gold standard is z, the number of phrases in the Lempel-Ziv parse of the text, which is the optimal one when phrases can be copied only from the left.  ...  We proceed by observing that Lempel-Ziv is just one particular case of greedy parses, meaning that the optimal value of z is obtained by scanning the text and maximizing the phrase length at each step,  ...  If j i = 0 we create an explicit symbol in the parse. Of course, particular greedy parses, like Lempel-Ziv, can be obtained faster, in this case in time O(n) [51] , [11] .  ... 
arXiv:1803.09517v2 fatcat:2w5jnh55b5gmnjuh5gftbq64ky

Optimal prefetching via data compression

Jeffrey Scott Vitter, P. Krishnan
1996 Journal of the ACM  
Our prediction algorithms for prefetching are novel in that they are based on data compression techniques that are both theoretically optimal and good in practice.  ...  In this paper, we apply a form of the competitive philosophy for the first time to the problem of prefetching to develop an optimal universal prefetcher in terms of fault rate, with particular applications  ...  The substrings in the parse can be denoted by a parse tree, like the one pictured in Figure 1 .  ... 
doi:10.1145/234752.234753 fatcat:uca2h5khtreqzp2fl2kp6w2cma

Variable-length extractors

Hongchao Zhou, Jehoshua Bruck
2012 2012 IEEE International Symposium on Information Theory Proceedings  
of statistical difference; and (ii) they minimize the expected number of symbols read from the source in order to reach a prescribed number of random bits.  ...  In this paper, we consider a scenario where the source is a weak stochastic process and the output sequence is required to be ϵ-close to the uniform distribution on {0, 1} m , where m is a prescribed value  ...  Here, we are interested in Lempel-Ziv code with fixed output-length and variable input-length.  ... 
doi:10.1109/isit.2012.6283024 dblp:conf/isit/ZhouB12 fatcat:46zl47zazjbwpfuvnd7ioeh53a

LZ77-Like Compression with Fast Random Access

Sebastian Kreft, Gonzalo Navarro
2010 2010 Data Compression Conference  
Most Lempel-Ziv parsings can decompress the text only from the beginning.  ...  We introduce an alternative Lempel-Ziv text parsing, LZ-End, that converges to the entropy and in practice gets very close to LZ77. LZ-End forces sources to finish at the end of a previous phrase.  ...  This is now feasible with LZ-End parsing, thus our next goal is to implement such a self-index. This would provide not only access to the compressed data, but also efficient indexed search.  ... 
doi:10.1109/dcc.2010.29 dblp:conf/dcc/KreftN10 fatcat:obhkr3krzbf47cygoux3vesstu
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