An online algorithm for lightweight grammar-based compression

Algorithms

Volumn 5, Issue 2, 2012, Pages 214-235

  Maruyama, Shirou ^a   Sakamoto, Hiroshi ^b   Takeda, Masayuki ^a  

^a KYUSHU UNIVERSITY   (Japan)

^b KYUSHU INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Approximation algorithm; Grammar based compression; Lossless compression; Online algorithm

Indexed keywords

APPROXIMATION RATIOS; COMPACT REPRESENTATION; GRAMMAR-BASED COMPRESSION; INPUT SIZE; LINEAR SPACES; LINEAR TIME; LOSSLESS COMPRESSION; ON-LINE ALGORITHMS;

APPROXIMATION ALGORITHMS;

EID: 84866929867     PISSN: None     EISSN: 19994893     Source Type: Journal    
DOI: 10.3390/a5020214     Document Type: Article

References (36)

1. Kieffer, J.; Yang, E.H. Grammar-based codes: A new class of universal lossless source codes. IEEE Trans. Inf. Theory 2000, 46, 737-754.
2. Ziv, J.; Lempel, A. A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 1977, 23, 337-343.
3. Sirẽn, J.; Välimäki, N.; Mäkinenn, V.; Navarro, G. Run-Length Compressed Indexes are Superior for Highly Repetitive Sequence Collections. In Proceedings of the 15th International Symposium on String Processing and Information Retrievals (SPIRE '08), Melbourne, Australia, 10-12 November 2008; pp. 164-175.
4. Claude, F.; Feriña, A.; Martinez-Prieto, M.A.; Navarro, G. Compressed q-Gram Indexing for Highly Repetitive Biological Sequences. In Proceedings of the 10th IEEE International Conference on Bioinformatics and Bioengineering (BIBE '10), Philadelphia, PA, USA, 31 May-3 June 2010; pp. 86-91.
5. Kreft, S.; Navarro, G. Self-Indexing Based on LZ77. In Proceedings of the 22th Annual Symposium on Combinatorial Pattern Matching (CPM '11), Palermo, Italy, 27-29 June 2011; pp. 285-298.
6. Karpinski, M.; Rytter, W.; Shinohara, A. An efficient pattern matching algorithm strings with short descriptions. Nordic J. Comput. 1997, 4, 172-186.
7. Miyazaki, M.; Shinohara, A.; Takeda, M. An Improved Pattern Matching Algorithm for Strings in Terms of Straight-Line Programs. In Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching (CPM '97), CPM 97, Aarhus, Denmark, 30 June-2 July 1997; volume 1264, pp. 1-11.
8. Cégielski, P.; Guessarian, I.; Lifshits, Y.; Matiyasevich, Y. Window Subsequence Problems for Compressed Texts. In Proceedings of the 1st International Computer Science Symposium in Russia (CSR '06), St. Petersburg, Russia, 8-12 June 2006; pp. 127-136.
9. Lifshits, Y. Processing Compressed Texts: A Tractability Border. In Proceedings of the 18th Annual Symposium on Combinatorial Pattern Matching (CPM '07), London, Canada, 9-11 July 2007; volume 4580, pp. 228-240.
10. Tiskin, A. Towards Approximate Matching in Compressed Strings. In Proceedings of the 6th International Computer Science Symposium in Russia (CSR '11), St. Petersburg, Russia, 14-18 June 2011; volume 6651, pp. 401-414.
11. Yamamoto, T.; Bannai, H.; Inenaga, S.; Takeda, M. Faster Subsequence and Don't-Care Pattern Matching on Compressed Texts. In Proceedings of the 22th Annual Symposium on Combinatorial Pattern Matching (CPM '11), Palermo, Italy, 27-29 June 2011; volume 6661, pp. 309-322.
12. Hermelin, D.; Landau, G.M.; Landau, S.; Weimann, O. A Unified Algorithm for Accelerating Edit-Distance Computation via Text-Compression In Proceedings of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS '09), Freiburg, Germany, 26-28 February 2009; pp. 529-540.
13. Goto, K.; Bannai, H.; Inenaga, S.; Takeda, M. Fast q-Gram Mining on SLP Compressed Strings. In Proceedings of the 18th International Symposium on String Processing and Information Retrieval (SPIRE '11), Pisa, Italy, 17-21 October 2011; volume 7028, pp. 278-289.
14. Goto, K.; Bannai, H.; Inenaga, S.; Takeda, M. Computing q-Gram Non-Overlapping Frequencies on SLP Compressed Texts. In Proceedings of the 38th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM '12), Spindlerv Mlýn, Czech Republic, 21-27 January 2012; pp. 301-312.
15. Inenaga, S.; Bannai, H. Finding Characteristic Substrings from Compressed Texts. In Proceedings of the Prague Stringology Conference (PSC '09), Prague, Czech Republic, 31 August- 2 September 2009; pp. 40-54.
16. Matsubara, W.; Inenaga, S.; Ishino, A.; Shinohara, A.; Nakamura, T.; Hashimoto, K. Efficient algorithms to compute compressed longest common substrings and compressed palindromes. Theor. Comput. Sci. 2009, 410, 900-913.
17. Lehman, E.; Shelat, A. Approximation Algorithms for Grammar-Based Compression. In Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '02), San Francisco, CA, USA, 6-8 January 2002; pp. 205-212.
18. Nevill-Manning, C.; Witten, I. Identifying hierarchical strcture in sequences: A linear-time algorithm. J. Artif. Intell. Res. 1997, 7, 67-82.
19. Larsson, N.; Moffat, A. Off-line dictionary-based compression. Proc. IEEE 2000, 88, 1722-1732.
20. Apostolico, A.; Lonardi, S. Offline compression by greedy textual substitution. Proc. IEEE 2000, 88, 1733-1744.
21. Nakamura, R.; Inenaga, S.; Bannai, H.; Funamoto, T.; Takeda, M.; Shinohara, A. Linear-time off-line text compression by longest-first substitution. Algorithms 2009, 2, 1429-1448.
22. Charikar, M.; Lehman, E.; Liu, D.; Panigrahy, R.; Prabhakaran, M.; Sahai, A.; Shelat, A. The smallest grammar problem. IEEE Trans. Inf. Theory 2005, 51, 2554-2576.
23. Rytter, W. Application of Lempel-Ziv factorization to the approximation of grammar-based compression. Theor. Comput. Sci. 2003, 302, 211-222.
24. Sakamoto, H. A fully linear-time approximation algorithm for grammar-based compression. J. Discret. Algorithms 2005, 3, 416-430.
25. Sakamoto, H.; Kida, T.; Shimozono, S. A Space-Saving Linear-Time Algorithm for Grammar-Based Compression. In Proceedings of the 11th International Symposium on String Processing and Information Retrieval (SPIRE '04), Padova, Italy, 5-8 October 2004; pp. 218-229.
26. Sakamoto, H.; Maruyama, S.; Kida, T.; Shimozono, S. A space-saving approximation algorithm for grammar-based compression. IEICE Trans. Inf. Syst. 2009, E92-D, 158-165.
27. Gagie, T.; Gawrychowski, P. Grammar-Based Compression in a Streaming Model. In Proceedings of the 4th International Conference on Language and Automata Theory and Applications (LATA '10), Trier, Germany, 24-28 May 2010; volume 6031, pp. 273-284.
28. Gusfield, D. Algorithms on Strings, Trees, and Sequences; Cambridge University Press: Cambridge, UK, 1997.
29. Dietzfelbinger, M.; Karlin, A.; Mehlhorn, K.; auf der Heide, F.M.; Rohnert, H.; Tarjan, R.E. Dynamic Perfect Hashing: Upper and Lower Bounds. In Proceedings of the 29th Annual Symposium on Foundations of Computer Science (FOCS '88), White Plains, New York, USA, 24-26 October 1988; pp. 524-531.
30. Welch, T. A technique for high-performance data compression. IEEE Comput. 1984, pp. 8-19.
31. Ziv, J.; Lempel, A. Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 1978, 24, 530-536.
32. Burrows, M.; Wheeler, D. A Block Sorting Lossless Data Compression Algorithm; Technical Report 124, Digital Equipment Corporation, 1994.
33. Kida, T.; Matsumoto, T.; Shibata, Y.; Takeda, M.; Shinohara, A.; Arikawa, S. Collage systems: A unifying framework for compressed pattern matching. Theor. Comput. Sci. 2003, 298, 253-272.
34. Claude, F.; Navarro, G. Self-Indexed Grammar-Based Compression. Fundam. Inform. 2011, 3, 313-337.
35. Gagie, T.; Gawrychowski, P.; Puglisi, S.J. Faster Grammar-Based Self-Index. In Proceedings of the 6th International Conference on Language and Automata Theory and Applications (LATA '12), A Coruña, Spain, 5-9 March 2012; pp. 273-284.
36. Bille, P.; Landau, G.M.; Raman, R.; Sadakane, K.; Satti, S.R.; Weimann, O. Random Access to Grammar-Compressed Strings. In Proceedings of the 22th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '11), San Francisco, California, USA, 23-25 January 2011; pp. 373-389.