A space-saving approximation algorithm for grammar-based compression

IEICE Transactions on Information and Systems

Volumn E92-D, Issue 2, 2009, Pages 158-165

  Sakamoto, Hiroshi ^a   Maruyama, Shirou ^b   Kida, Takuya ^c   Shimozono, Shinichi ^a  

^a KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

^b KYUSHU UNIVERSITY   (Japan)

^c HOKKAIDO UNIVERSITY   (Japan)

Author keywords

Approximation algorithm; Grammar based compression; Minimum cfg problem

Indexed keywords

CONTEXT FREE GRAMMARS;

APPROXIMATION RATIOS; BEST APPROXIMATIONS; GRAMMAR-BASED COMPRESSION; INPUT LENGTHS; MINIMUM CFG PROBLEM; SPACE EFFICIENT; SPACE SAVINGS;

APPROXIMATION ALGORITHMS;

EID: 77950238328     PISSN: 09168532     EISSN: 17451361     Source Type: Journal    
DOI: 10.1587/transinf.E92.D.158     Document Type: Article

References (24)

1. G. Ausiello, P. Crescenzi, G. Gambosi, V. Kann, A. Marchetti-Spaccamela, and M. Protasi, Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties, Springer, 1999.
2. S. De Agostino and J. A. Storer, "On-line versus off-line computation in dynamic text compression, " Inf. Process. Lett., vol. 59, pp. 169-174, 1996.
3. A. Apostolico and S. Lonardi, "Some theory and practice of greedy off-line textual substitution, " Proc. Data Compression Conference 1998, pp. 119-128, 1998.
4. M. Charikar, E. Lehman, D. Liu, R. Panigrahy, M. Prabhakaran, A. Rasala, A. Sahai, and A. Shelat, "The smallest grammar problem, " IEEE Trans. Inf. Theory, vol. 51, no. 7, pp. 2554-2576, 2005.
5. G. Cormode and S. Muthukrishnan, "The string edit distance matching problem with moves, " ACM Trans. Algorithms, vol. 3, no. 1, article 2, 2007.
6. T. Kida, T. Matsumoto, Y. Shibata, M. Takeda, A. Shinohara, and S. Arikawa, "Collage system: A unifying framework for compressed pattern matching, " Theor. Comput. Sci., vol. 298, no. 1, pp. 253-272, 2003.
7. J. C. Kieffer and E.-H. Yang, "Grammar-based codes: A new class of universal lossless source codes, " IEEE Trans. Inf. Theory, vol. 46, no. 3, pp. 737-754, 2000.
8. J. C. Kieffer, E.-H. Yang, G. Nelson, and P. Cosman, "Universal lossless compression via multilevel pattern matching, " IEEE Trans. Inf. Theory, vol. 46, no. 5, pp. 1227-1245, 2000.
9. D. Knuth, The Art of Computer Programming, Volume II: Seminumerical Algorithms, Addison-Wesley, 1981.
10. N. J. Larsson and A. Moffat, "Offline dictionary-based compression, " Proc. IEEE, vol. 88, no. 11, pp. 1722-1732, 2000.
11. J. van Leeuwen, (Managing Editor). Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity, Elsevier, 1998.
12. E. Lehman, Approximation Algorithms for Grammar-Based Compression. PhD thesis, MIT, 2002.
13. E. Lehman and A. Shelat, "Approximation algorithms for grammarbased compression, " Proc. 20th Ann. ACM-SIAM Sympo. Discrete Algorithms, pp. 205-212, 2002.
14. S. Maruyama, H. Miyagawa, and H. Sakamoto, "Improving time and space complexity for compressed pattern matching, " Proc. 17th Int. Sympo. Algorithms and Computation, LNCS4288, pp. 484-493, 2006.
15. C. Nevill-Manning and I. Witten, "Compression and explanation using hierarchical grammars, " Comput. J., vol. 40, no. 2/3, pp. 103-116, 1997.
16. C. Nevill-Manning and I. Witten, "Identifying hierarchical structure in sequences: A linear-time algorithm, " J. Artificial Intelligence Research, vol. 7, pp. 67-82, 1997.
17. W. Rytter, "Application of Lempel-Ziv factorization to the approximation of grammar-based compression, " Theor. Comput. Sci., vol. 302, no. 1-3, pp. 211-222, 2003.
18. H. Sakamoto, T. Kida, and S. Shimozono, "A space-saving lineartime algorithm for grammar-based compression, " Proc. 11th International Symposium on String Processing and Information Retrieval, LNCS3109, pp. 218-229, 2004.
19. H. Sakamoto, "A fully linear-time approximation algorithm for grammar-based compression, " J. Discrete Algorithms, vol. 3, no. 2-4, pp. 416-430, 2005.
20. J. A. Storer and T. G. Szymanski, "The macro model for data compression, " Proc. 10th Ann. Sympo. Theory of Computing, pp. 30-39, 1978.
21. T. A. Welch, "A technique for high performance data compression, " Computer, vol. 17, pp. 8-19, 1984.
22. E.-H. Yang and J. C. Kieffer, "Efficient universal lossless data compression algorithms based on a greedy sequential grammar transform-part one: Without context models, " IEEE Trans. Inf. Theory, vol. 46, no. 3, pp. 755-777, 2000.
23. J. Ziv and A. Lempel, "A universal algorithm for sequential data compression, " IEEE Trans. Inf. Theory, vol. IT-23, no. 3, pp. 337-349, 1977.
24. J. Ziv and A. Lempel, "Compression of individual sequences via variable-rate coding, " IEEE Trans. Inf. Theory, vol. IT-24, no. 5, pp. 530-536, 1978.