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Asymptotic Behavior of the Height in a Digital Search Tree and the Longest Phrase of the LempelZiv Scheme
, 1999
"... ..."
On Generalized Digital Search Trees With Applications To A Generalized LempelZiv Algorithm
, 1995
"... The goal of this research is twofold: (i) to analyze generalized digital search trees, and (ii) to derive the average profile (i.e., phrase length) of a generalization of the well known parsing algorithm due to Lempel and Ziv. In the generalized LempelZiv parsing scheme, one partitions a sequence o ..."
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of symbols from a finite alphabet into phrases such that the new phrase is the longest substring seen in the past by at most b \Gamma 1 phrases. The case b = 1 corresponds to the original LempelZiv scheme. As expected, such a scheme can be analyzed by considering a generalized digital search tree in which
Asymptotic Behavior of the LempelZiv Parsing Scheme and Digital Search Trees
 Theoretical Computer Science
, 1995
"... The LempelZiv parsing scheme finds a wide range of applications, most notably in data compression and algorithms on words. It partitions a sequence of length n into variable phrases such that a new phrase is the shortest substring not seen in the past as a phrase. The parameter of interest is the n ..."
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Cited by 72 (34 self)
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The LempelZiv parsing scheme finds a wide range of applications, most notably in data compression and algorithms on words. It partitions a sequence of length n into variable phrases such that a new phrase is the shortest substring not seen in the past as a phrase. The parameter of interest
LempelZiv Compressed FullText SelfIndexes
, 2009
"... Because of the many growing text collections available from different sources, the fulltext search problem arises in a wealth of applications, which need to provide efficient access to large text collections. Classical text indexes require much space (besides storing the text itself), and thus migh ..."
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of their efficiency. In this thesis we carry out a deep study of compressed fulltext selfindexes based on LempelZiv compression (LZindexes for short), contributing with new developments in this area. We base our study on Navarro’s LZindex (or simply LZindex). Before our work, the LZindexes were an attractive
On The Average Redundancy Rate Of The LempelZiv Code
 IEEE Trans. Inform. Theory
, 1996
"... In this paper, we settle a long standing open problem concerning the average redundancy, r n , of the LempelZiv'78 (LZ78) code. We prove that for a memoryless source the average redundancy rate attains asymptotically Er n = (A + ffi(n))= log n + O(log log n= log 2 n), where A is an explici ..."
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Cited by 26 (4 self)
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. The main result of this paper is a consequence of recently obtained secondorder properties of the LempelZiv algorithm [P. Jacquet, W. Szpankowski, Theoretical Computer Science, 144, 1995]. These findings have been established by analytical techniques of the precise analysis of algorithms. We give a brief
Longestmatch String Searching for ZivLempel Compression
, 1993
"... This paper presents eight data structures that can be used to accelerate the searching, including adaptations of four methods normally used for exact matching searching. The algorithms are evaluated analytically and empirically, indicating the tradeoffs available between compression speed and memor ..."
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Cited by 18 (2 self)
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and memory consumption. Two of the algorithms are wellknown methods of finding the longest matchthe timeconsuming linear search, and the storageintensive trie (digital search tree). The trie is adapted along the lines of a PATRICIA tree to operate economically. Hashing, binary search trees, splay trees
On the bitcomplexity of LempelZiv compression
"... 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 “dictionarybased compressor ” and consists of squeezing an input string by replacing some of its substrings with (shorter) c ..."
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Cited by 9 (2 self)
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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 “dictionarybased compressor ” and consists of squeezing an input string by replacing some of its substrings with (shorter
Average Profile Of The LempelZiv Parsing Scheme For A Markovian Source
 Algorithmica
, 1998
"... For a Markovian source, we analyze the LempelZiv parsing scheme that partitions sequences into phrases such that a new phrase is the shortest phrase not seen in the past. We consider three models: In the Markov Independent model, several sequences are generated independently by Markovian sources, ..."
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Cited by 23 (14 self)
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For a Markovian source, we analyze the LempelZiv parsing scheme that partitions sequences into phrases such that a new phrase is the shortest phrase not seen in the past. We consider three models: In the Markov Independent model, several sequences are generated independently by Markovian sources
Smaller and Faster LempelZiv Indices?
"... 1 Introduction With the huge amount of text data available nowadays, the fulltext searchingproblem plays a fundamental role in modern computer applications. Fulltext searching consists of finding the occ occurrences of a given pattern P [1..m]in a text T [1..u], where both P and T are sequences ov ..."
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1 Introduction With the huge amount of text data available nowadays, the fulltext searchingproblem plays a fundamental role in modern computer applications. Fulltext searching consists of finding the occ occurrences of a given pattern P [1..m]in a text T [1..u], where both P and T are sequences
Stronger LempelZiv Based Compressed Text Indexing
, 2008
"... Given a text T[1..u] over an alphabet of size σ, the fulltext search problem consists in finding the occ occurrences of a given pattern P[1..m] in T. In indexed text searching we build an index on T to improve the search time, yet increasing the space requirement. The current trend in indexed text ..."
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Cited by 19 (8 self)
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) worstcase time. Despite this index has shown to be very competitive in practice, the O(m 3 log σ) term can be excessive for long patterns. Also, the factor 4 in its space complexity makes it larger than other stateoftheart alternatives. In this paper we present stronger LempelZiv based indices
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