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

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 ...

##
###
Lempel–Ziv-Like Parsing in Small Space

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 ...

##
###
Data Compression Support in Databases

1994
*
Very Large Data Bases Conference
*

Roughly speaking, a slight increase

dblp:conf/vldb/IyerW94
fatcat:5atidjxm4rdazgodd4zlbk4rci
*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 ...##
###
On the average redundancy rate of the Lempel-Ziv code

1997
*
IEEE Transactions on Information Theory
*

,

doi:10.1109/18.567640
fatcat:hg7iozitwzhedow2dgn2hcmthm
*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. ...##
###
Approximating Optimal Bidirectional Macro Schemes
[article]

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*. ...

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

2018
*
Lecture Notes in Computer Science
*

Since computing b is NP-complete, a popular gold standard is z, the number of phrases

doi:10.1007/978-3-319-77404-6_36
fatcat:lqhuqs3ohbht5dsx3wtorpmgdy
*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 . . . ...##
###
Pushdown Compression

2008
*
Symposium on Theoretical Aspects of Computer Science
*

We prove that

doi:10.4230/lipics.stacs.2008.1332
dblp:conf/stacs/AlbertMMP08
fatcat:ipybgu6r5nbatjnbwrhbodb7pa
*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. ...##
###
A Lempel-Ziv like approach for signal classification

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 . ...

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

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

doi:10.1007/978-3-540-95891-8_56
fatcat:o5jbvscdq5gk5d7l2n27wf6l7y
*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] . ...##
###
Indexing Highly Repetitive String Collections
[article]

2022
*
arXiv
*
pre-print

Two decades ago, a breakthrough

arXiv:2004.02781v9
fatcat:rceyc6ti5jdfpebkrbbgq3kine
*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). ...##
###
Average Profile of the Generalized Digital Search Tree and the Generalized Lempel--Ziv Algorithm

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. ...

##
###
On the Approximation Ratio of Ordered Parsings
[article]

2019
*
arXiv
*
pre-print

Since computing b is NP-complete, a popular gold standard is z, the number of phrases

arXiv:1803.09517v2
fatcat:2w5jnh55b5gmnjuh5gftbq64ky
*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] . ...##
###
Optimal prefetching via data compression

1996
*
Journal of the ACM
*

Our prediction algorithms for prefetching are novel

doi:10.1145/234752.234753
fatcat:uca2h5khtreqzp2fl2kp6w2cma
*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 . ...##
###
Variable-length extractors

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

doi:10.1109/isit.2012.6283024
dblp:conf/isit/ZhouB12
fatcat:46zl47zazjbwpfuvnd7ioeh53a
*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. ...##
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LZ77-Like Compression with Fast Random Access

2010
*
2010 Data Compression Conference
*

Most

doi:10.1109/dcc.2010.29
dblp:conf/dcc/KreftN10
fatcat:obhkr3krzbf47cygoux3vesstu
*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. ...
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