An LZ78 Based String Kernel

Li, Ming; Sleep, Ronan

doi:10.1007/11527503_80

Cited by 13 publications

(3 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since main memory sizes of ordinary computers do not scale as fast as the growth of datasets, insufficient memory is a well-aware problem; both huge mainframes with massive datasets and tiny embedded systems are valid examples for which a simple compressor may end up depleting all RAM. Besides, they have also been found to be a valuable tool for detecting various kinds of regularities in strings [4,6,14,[21][22][23]26], for indexing [7,10,11,18,19,31] and for analyzing strings [5,24,25].…”

Section: Introductionmentioning

confidence: 99%

Lempel Ziv Computation in Small Space (LZ-CISS)

Fischer

Tomohiro

Köppl

2015

Combinatorial Pattern Matching

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Lempel Ziv Computation in Small Space (LZ-CISS)

Fischer

Tomohiro

Köppl

2015

Combinatorial Pattern Matching

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Constructing LZ78 tries and position heaps in linear time for large alphabets

Nakashima

Tomohiro

Inenaga

et al. 2015

Information Processing Letters

View full text Add to dashboard Cite

We present the first worst-case linear-time algorithm to compute the Lempel-Ziv 78 factorization of a given string over an integer alphabet. Our algorithm is based on nearest marked ancestor queries on the suffix tree of the given string. We also show that the same technique can be used to construct the position heap of a set of strings in worst-case linear time, when the set of strings is given as a trie.

show abstract

“…LZ78 compresses a given text based on a dynamic dictionary which is constructed by partitioning the input string, the process of which is called LZ78 factorization. Other than its obvious use for compression, the LZ78 factorization is an important concept used in various string processing algorithms and applications [7,19,18,20]. The contribution of this paper is an O(n √ N + m log N ) time and O(n √ N + m) space algorithm to compute the LZ78 factorization of a string given as an SLP, where N is the length of the string, n is the size of the SLP, and m is the number of LZ78 factors.…”

Section: Introductionmentioning

confidence: 99%

Efficient LZ78 Factorization of Grammar Compressed Text

Bannai

Inenaga

Takeda

2012

String Processing and Information Retrieval

View full text Add to dashboard Cite

Abstract. We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string. Given an SLP of size n representing a text S of length N , our algorithm computes the LZ78 factorization ofwhere m is the number of resulting LZ78 factors. We also show how to improve the algorithm so that the n √ N term in the time and space complexities becomes either nL, where L is the length of the longest LZ78 factor, or (N − α) where α ≥ 0 is a quantity which depends on the amount of redundancy that the SLP captures with respect to substrings of S of a certain length. Since m = O(N/ log σ N ) where σ is the alphabet size, the latter is asymptotically at least as fast as a linear time algorithm which runs on the uncompressed string when σ is constant, and can be more efficient when the text is compressible, i.e. when m and n are small.

show abstract

An LZ78 Based String Kernel

Cited by 13 publications

References 10 publications

Lempel Ziv Computation in Small Space (LZ-CISS)

Lempel Ziv Computation in Small Space (LZ-CISS)

Constructing LZ78 tries and position heaps in linear time for large alphabets

Efficient LZ78 Factorization of Grammar Compressed Text

Contact Info

Product

Resources

About