On two LZ78-style grammars: Compression bounds and compressed-space computation

Golnaz Badkobeh, Travis Gagie, Shunsuke Inenaga, Tomasz Kociumaka, Dmitry Kosolobov, Simon J. Puglisi

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

1 Citation (Scopus)

Abstract

We investigate two closely related LZ78-based compression schemes: LZMW (an old scheme by Miller and Wegman) and LZD (a recent variant by Goto et al.). Both LZD and LZMW naturally produce a grammar for a string of length n; we show that the size of this grammar can be larger than the size of the smallest grammar by a factor Ω(n1/3) but is always within a factor (Formula presented). In addition, we show that the standard algorithms using Θ(z) working space to construct the LZD and LZMW parsings, where z is the size of the parsing, work in Ω(n5/4) time in the worst case. We then describe a new Las Vegas LZD/LZMW parsing algorithm that uses O(z log n) space and O(n + zlog2n) time w.h.p.

Original languageEnglish
Title of host publicationString Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Proceedings
EditorsRossano Venturini, Gabriele Fici, Marinella Sciortino
PublisherSpringer Verlag
Pages51-67
Number of pages17
ISBN (Print)9783319674278
DOIs
Publication statusPublished - Jan 1 2017
Event24th International Symposium on String Processing and Information Retrieval, SPIRE 2017 - Palermo, Italy
Duration: Sep 26 2017Sep 29 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10508 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other24th International Symposium on String Processing and Information Retrieval, SPIRE 2017
CountryItaly
CityPalermo
Period9/26/179/29/17

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Badkobeh, G., Gagie, T., Inenaga, S., Kociumaka, T., Kosolobov, D., & Puglisi, S. J. (2017). On two LZ78-style grammars: Compression bounds and compressed-space computation. In R. Venturini, G. Fici, & M. Sciortino (Eds.), String Processing and Information Retrieval - 24th International Symposium, SPIRE 2017, Proceedings (pp. 51-67). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10508 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-67428-5_5