LZD factorization: Simple and practical online grammar compression with variable-to-fixed encoding

Keisuke Goto, Hideo Bannai, Shunsuke Inenaga, Masayuki Takeda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Citations (Scopus)

Abstract

We propose a new variant of the LZ78 factorization which we call the LZ Double-factor factorization (LZD factorization). Each factor of the LZD factorization of a string is the concatenation of the two longest previous factors, while each factor of the LZ78 factorization is that of the longest previous factor and the following character. Interestingly, this simple modification drastically improves the compression ratio in practice. We propose two online algorithms to compute the LZD factorization in O(m(M +min(m, M) log σ)) time and O(m) space, or in O(N log σ) time and O(N) space, where m is the number of factors to output, M is the length of the longest factor(s), N is the length of the input string, and σ is the alphabet size. We also show two versions of our LZD factorization with variable-to-fixed encoding, and present online algorithms to compute these versions in O(N + min(m, 2L)(M + min(m, M, 2L) log σ)) time and O(min(2L, m)) space, where L is the bit-length of each fixed-length code word. The LZD factorization and its versions with variable-to fixed encoding are actually grammar-based compression, and our experiments show that our algorithms outperform the state-of-the-art online grammar-based compression algorithms on several data sets.

Original languageEnglish
Title of host publicationCombinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings
EditorsUgo Vaccaro, Ely Porat, Ferdinando Cicalese
PublisherSpringer Verlag
Pages219-230
Number of pages12
ISBN (Print)9783319199283
DOIs
Publication statusPublished - 2015
Event26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015 - Ischia Island, Italy
Duration: Jun 29 2015Jul 1 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9133
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other26th Annual Symposium on Combinatorial Pattern Matching, CPM 2015
CountryItaly
CityIschia Island
Period6/29/157/1/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Goto, K., Bannai, H., Inenaga, S., & Takeda, M. (2015). LZD factorization: Simple and practical online grammar compression with variable-to-fixed encoding. In U. Vaccaro, E. Porat, & F. Cicalese (Eds.), Combinatorial Pattern Matching - 26th Annual Symposium, CPM 2015, Proceedings (pp. 219-230). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9133). Springer Verlag. https://doi.org/10.1007/978-3-319-19929-0_19