Skip to main content
SpringerLink
Log in
Book cover

International Symposium on String Processing and Information Retrieval

SPIRE 2004: String Processing and Information Retrieval pp 218–229Cite as

A Space-Saving Linear-Time Algorithm for Grammar-Based Compression

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3246))

Abstract

A space-efficient linear-time approximation algorithm for the grammar-based compression problem, which requests for a given string to find a smallest context-free grammar deriving the string, is presented. The algorithm consumes only O(g * log g *) space and achieves the worst-case approximation ratio O(log g * log n), with the size n of an input and the optimum grammar size g *. Experimental results for typical benchmarks demonstrate that our algorithm is practical and efficient.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer, Heidelberg (1999)

    MATH  Google Scholar 

  2. De Agostino, S., Storer, J.A.: On-Line versus Off-Line Computation in Dynamic Text Compression. Inform. Process. Lett. 59, 169–174 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Charikar, M., Lehman, E., Liu, D., Panigrahy, R., Prabhakaran, M., Rasala, A., Sahai, A., Shelat, A.: Approximating the Smallest Grammar: Kolmogorov Complexity in Natural Models. In: Proc. 29th Ann. Sympo. on Theory of Computing, pp. 792–801 (2002)

    Google Scholar 

  4. Farach, M.: Optimal Suffix Tree Construction with Large Alphabets. In: Proc. 38th Ann. Sympo. on Foundations of Computer Science, pp. 137–143 (1997)

    Google Scholar 

  5. Gusfield, D.: Algorithms on Strings, Trees, and Sequences. In: Computer Science and Computational Biology, Cambridge University Press, Cambridge (1997)

    Google Scholar 

  6. Kida, T., Shibata, Y., Takeda, M., Shinohara, A., Arikawa, S.: Collage System: a Unifying Framework for Compressed Pattern Matching. Theoret. Comput. Sci. (to appear)

    Google Scholar 

  7. Kieffer, J.C., Yang, E.-H.: Grammar-Based Codes: a New Class of Universal Lossless Source Codes. IEEE Trans. on Inform. Theory 46(3), 737–754 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Kieffer, J.C., Yang, E.-H., Nelson, G., Cosman, P.: Universal Lossless Compression via Multilevel Pattern Matching. IEEE Trans. Inform. Theory IT-46(4), 1227–1245 (2000)

    Article  MathSciNet  Google Scholar 

  9. Knuth, D.: Seminumerical Algorithms, pp. 441–462. Addison-Wesley, Reading (1981)

    MATH  Google Scholar 

  10. Larsson, N.J., Moffat, A.: Offline Dictionary-Based Compression. Proceedings of the IEEE 88(11), 1722–1732 (2000)

    Article  Google Scholar 

  11. Lehman, E.: Approximation Algorithms for Grammar-Based Compression. PhD thesis, MIT (2002)

    Google Scholar 

  12. Lehman, E., Shelat, A.: Approximation Algorithms for Grammar-Based Compression. In: Proc. 20th Ann. ACM-SIAM Sympo. on Discrete Algorithms, pp. 205–212 (2002)

    Google Scholar 

  13. Lothaire, M.: Combinatorics on Words. Encyclopedia of Mathematics and Its Applications, vol. 17. Addison-Wesley, Reading (1983)

    MATH  Google Scholar 

  14. Nevill-Manning, C., Witten, I.: Compression and Explanation Using Hierarchical Grammars. Computer Journal 40(2/3), 103–116 (1997)

    Article  Google Scholar 

  15. Nevill-Manning, C., Witten, I.: Identifying hierarchical structure in sequences: a linear-time algorithm. J. Artificial Intelligence Research 7, 67–82 (1997)

    MATH  Google Scholar 

  16. Rytter, W.: Application of Lempel-Ziv Factorization to the Approximation of Grammar-Based Compression. In: Proc. 13th Ann. Sympo. Combinatorial Pattern Matching, pp. 20–31 (2002)

    Google Scholar 

  17. Sakamoto, H.: A Fully Linear-Time Approximation Algorithm for Grammar-Based Compression. Journal of Discrete Algorithms (to appear)

    Google Scholar 

  18. Salomon, D.: Data compression: the complete reference, 2nd edn. Springer, Heidelberg (1998)

    Google Scholar 

  19. Storer, J., Szymanski, T.: Data compression via textual substitution. J. Assoc. Comput. Mach. 29(4), 928–951 (1982)

    MATH  MathSciNet  Google Scholar 

  20. Storer, J.A., Szymanski, T.G.: The Macro Model for Data Compression. In: Proc. 10th Ann. Sympo. on Theory of Computing, San Diego, California, pp. 30–39. ACM Press, New York (1978)

    Chapter  Google Scholar 

  21. Welch, T.A.: A Technique for High Performance Data Compression. IEEE Comput. 17, 8–19 (1984)

    Google Scholar 

  22. Yang, E.-H., Kieffer, J.C.: Efficient Universal Lossless Data Compression Algorithms Based on a Greedy Sequential Grammar Transform–Part One: without Context Models. IEEE Trans. on Inform. Theory 46(3), 755–777 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  23. Ziv, J., Lempel, A.: A Universal Algorithm for Sequential Data Compression. IEEE Trans. on Inform. Theory IT-23(3), 337–349 (1977)

    Article  MathSciNet  Google Scholar 

  24. Ziv, J., Lempel, A.: Compression of Individual Sequences via Variable-Rate Coding. IEEE Trans. on Inform. Theory 24(5), 530–536 (1978)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kyushu Institute of Technology, Kawazu 680-4, Iizuka, 820-8502, Japan

    Hiroshi Sakamoto & Shinichi Shimozono

  2. Hokkaido University, Kita 14, Nishi 9, Kita-ku, Sapporo, 060-0814, Japan

    Takuya Kida

Authors
  1. Hiroshi Sakamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Takuya Kida
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shinichi Shimozono
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Georgia Institute of Technology and Università di Padova,  

    Alberto Apostolico

  2. Department of Information Engineering, University of Padova,  

    Massimo Melucci

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sakamoto, H., Kida, T., Shimozono, S. (2004). A Space-Saving Linear-Time Algorithm for Grammar-Based Compression. In: Apostolico, A., Melucci, M. (eds) String Processing and Information Retrieval. SPIRE 2004. Lecture Notes in Computer Science, vol 3246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30213-1_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-30213-1_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23210-0

  • Online ISBN: 978-3-540-30213-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation