Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
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چکیده
منابع مشابه
Asymptotic Behavior of the Lempel-Ziv Parsing Scheme and Digital Search Trees
The Lempel-Ziv 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 number M n of phrases that one can construct from a sequence of length n. In this paper, for the m...
متن کاملAsymptotic Behavior of the Height in a Digital Search Tree and the Longest Phrase of the Lempel-Ziv Scheme
Wojciech Szpankowskit Department of Computer Science Purdue University W. Lafayette, IN 47907 U.S.A. spa~cs.purdue.edu We study the height of a digital search tree (DST in short) built from n random strings generated by an unbiased memoryless source (i.e., all symbols are equally likely). We shall argue that the height of such a tree is equivalent to the length of the longest phrase in the Lemp...
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We introduce a new approach to LZ77 factorization that uses O(n/d) words of working space and O(dn) time for any d ≥ 1 (for polylogarithmic alphabet sizes). We also describe carefully engineered implementations of alternative approaches to lightweight LZ77 factorization. Extensive experiments show that the new algorithm is superior in most cases, particularly at the lowest memory levels and for...
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For a Markovian source, we analyze the Lempel-Ziv 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, and the ith phrase is the shortest preex of the ith sequence that was not seen before as a phrase ...
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We present an algorithm that computes the Lempel-Ziv decomposition in O(n(log σ+log log n)) time and n log σ+ǫn bits of space, where ǫ is a constant rational parameter, n is the length of the input string, and σ is the alphabet size. The n log σ bits in the space bound are for the input string itself which is treated as read-only.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1995
ISSN: 0304-3975
DOI: 10.1016/0304-3975(94)00298-w