Random access to grammar-compressed strings

Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Volumn , Issue , 2011, Pages 373-389

  Bille, Philip ^a   Landau, Gad M ^b,g   Raman, Rajeev ^c   Sadakane, Kunihiko ^d   Satti, Srinivasa Rao ^e   Weimann, Oren ^f  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b UNIVERSITY OF HAIFA   (Israel)

^c UNIVERSITY OF LEICESTER   (United Kingdom)

^d NATIONAL INSTITUTE OF INFORMATICS   (Japan)

^e Seoul National University   (South Korea)

^f WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^g POLYTECHNIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONTEXT FREE GRAMMARS; DATA STRUCTURES;

ACKERMANN'S FUNCTIONS; APPROXIMATE STRING MATCHING; COMPACT REPRESENTATION; CONSTRUCTION TIME; FAST ALGORITHMS; HEAVY PATH; POINTER MACHINES; RANDOM ACCESS;

RANDOM ACCESS STORAGE;

EID: 79955718122     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1137/1.9781611973082.30     Document Type: Conference Paper

References (61)

1. N. Alon and B. Schieber. Optimal preprocessing for answering on-line product queries. Technical report, TR-71/87, Institute of Computer Science, Tel Aviv University, 1987.
2. S. AIstrup, T. Husfeldt, and T. Rauhe. Marked ancestor problems. In Proceedings of the 39th annual symposium on Foundations Of Computer Science (FOCS), pages 534-543, 1998.
3. A. Amir, G. Benson, and M. Farach. Let sleeping files lie: Pattern matching in Z-compressed files. Journal of Comp, and Sys. Sciences, 52(2):299-307, 1996. (Pubitemid 126375142)
4. A. Amir, G. Landau, and D. Sokol. Inplace 2d matching in compressed images. In Proc. of the 14th annual ACM-SIAM Symposium On Discrete Algorithms, (SODA), pages 853-862, 2003.
5. A. Amir, M. Lewenstein, and E. Porat. Faster algorithms for string matching with k mismatches. J. Algorithms, 50(2):257-275, 2004. Announced at SODA 2000.
6. A. Apostolico and S. Lonardi. Some theory and practice of greedy off-line textual substitution. In Proc. IEEE Data compression conference, pages 119-128, 1998.
7. A. Apostolico and S. Lonardi. Compression of biological sequences by greedy off-line textual substitution. In Proc. IEEE Data compression conference, pages 143-152, 2000. (Pubitemid 30588742)
8. A. Apostolico and S. Lonardi. Off-line compression by greedy textual substitution. Proc. IEEE, 88(11):1733-1744, 2000.
9. O. Arbell, G. M. Landau, and J. Mitchell. Edit distance of run-length encoded strings. Information Processing Letters, 83(6):307-314, 2001.
10. A. Bagchi, A. L. Buchsbaum, and M. Goodrich. Biased skip lists. Algorithmica, 42:31-48, 2005.
11. S. W. Bent, D. D. Sleator, and R. E. Tarjan. Biased search trees. SIAM J. Comput., 14(3):545-568, 1985.
12. P. Bille, R. Fagerberg, and I. L. Gørtz. Improved approximate string matching and regular expression matching on ziv-lempel compressed texts. ACM Transactions on Algorithms. To appear. Announced at CPM 2007.
13. P. Buneman, B. Choi, W. Fan, R. Hutchison, R. Mann, and S. Viglas. Vectorizing and querying large xml repositories. In ICDE, pages 261-272. IEEE Computer Society, 2005. (Pubitemid 41731139)
14. H. Bunke and J. Csirik. An improved algorithm for computing the edit distance of run length coded strings. Information Processing Letters, 54:93-96, 1995.
15. G. Busatto, M. Lohrey, and S. Maneth. Efficient memory representation of xml document trees. Inf. Syst., 33(4-5).456-474, 2008.
16. P. Cégielski, I. Guessarian, Y. Lifshits, and Y. Matiyasevich. Window subsequence problems for compressed texts. In Proc. of the 1st symp. on Computer Science in Russia (CSR), pages 127-136, 2006. (Pubitemid 44055071)
17. M. Charikar, E. Lehman, D. Liu, R. Panigrahy, M. Prabhakaran, A. Sahai, and A. Shelat. The smallest grammar problem. IEEE Transactions on Information Theory, 51(7):2554-2576, 2005. An-nounced at STOC 2002 and SODA 2002. (Pubitemid 41148951)
18. B. Chazelle and B. Rosenberg. Computing partial sums in multidimensional arrays. In Proceedings of the 5th annual ACM Symposium on Computational Geometry (SCG), pages 131-139, 1989.
19. F. Claude and G. Navarro. Self-indexed text compression using straight-line programs. In Proc. 34th Mathematical Foundations of Computer Science, volume 5734 of Lecture Notes in Computer Science, pages 235-246, 2009.
20. R. Cole and R. Hariharan. Approximate string matching: A simpler faster algorithm. SIAM J. Comput., 31(6):1761-1782, 2002.
21. M. Crochemore, G. Landau, and M. Ziv-Ukelson. A subquadratic sequence alignment algorithm for unrestricted scoring matrices. SIAM Journal on Computing, 32:1654-1673, 2003.
22. O. Delpratt, R. Raman, and N. Rahman. Engineering succinct doin. In A. Kemper, P. Val-duriez, N. Mouaddib, J. Teubner, M. Bouzeghoub, V. Markl, L. Amsaleg, and I. Manolescu, editors, EDBT, volume 261 of ACM International Conference Proceeding Series, pages 49-60. ACM, 2008.
23. F. Ellen. Constant-time operations for words of length w. 1999.
24. M. Farach and S. Muthukrishnan. Perfect hashing for strings: Formalization and algorithms. In Proceedings of the 7th Symposium on Combinatorial Pattern Matching (CPM), pages 130-140. Springer, 1996. (Pubitemid 126073715)
25. P. Ferragina, F. Luccio, G. Manzini, and S. Muthukrishnan. Compressing and indexing labeled trees, with applications. J. ACM, 57(1), 2009.
26. M. L. Fredman and D. E. Willard. Surpassing the information theoretic bound with fusion trees. J. Comput. Syst. Sci., 47(3):424-436, 1993.
27. M. L. Fredman and D. E. Willard. Trans- dichotomous algorithms for minimum spanning trees and shortest paths. J. Comput. Syst. Sci., 48(3):533-551, 1994. (Pubitemid 124013302)
28. P. Gage. A new algorithm for data compression. The C Users J., 12(2):23 - 38, 1994.
29. L. Gasieniec, R. Kolpakov, I. Potapov, and P. Sant. Real-time traversal in grammar-based compressed files. In Proceedings of the Data Compression Conference, pages 458-458, 2005.
30. L. Gasieniec and I. Potapov. Time/space efficient compressed pattern matching. Fundam. Inf., 56(1, 2):137-154, 2003.
31. T. Hagerup. Sorting and searching on the word rain. In M. Morvan, C. Meinel, and D. Krob, editors, STACS, volume 1373 of Lecture Notes in Computer Science, pages 366-398. Springer, 1998.
32. D. Harel and R. E. Tarjan. Fast algorithms for finding nearest common ancestors. SIAM J. Comput., 13(2):338-355, 1984. (Pubitemid 15493878)
33. D. Hermelin, S. Landau, G. Landau, and O. Weimann. A unified algorithm for accelerating edit-distance via text-compression. In Proc. of the 26th International Symposium on Theoretical Aspects of Computer Science (STACS), pages 529-540, 2009.
34. J. Iacono. private communication. 2010.
35. J. Karkkainen, G. Navarro, and E. Ukkonen. Approximate string matching over Ziv-Lempel compressed text. In Proc. of the 11th symposium on Combinatorial Pattern Matching (CPM), pages 195-209, 2000.
36. J. Karkkainen and E. Ukkonen. Lempel-Ziv parsing and sublinear-size index structures for string matching. In Proc. of the 3rd South American Workshop on String Processing (WSP), pages 141-155, 1996.
37. J. C. Kieffer and E. H. Yang. Grammar based codes: A new class of universal lossless source codes. IEEE Trans. Inf. Theory, 46(3) :737-754, 2000.
38. J. C. Kieffer, E. H. Yang, G. J. Nelson, and P. Cos-man. Universal lossless compression via multilevel pattern matching. IEEE Trans. Inf. Theory, 46(5): 1227 - 1245, 2000.
39. D. E. Knuth. Optimum binary search trees. Acta Informatica, 1:14-25, 1971.
40. G. M. Landau and U. Vishkin. Fast parallel and serial approximate string matching. J. Algorithms, 10(2):157-169, 1989.
41. J. N. Larsson and A. Moffat. Off-line dictionary- based compression. Proc. IEEE, 88(11):1722 - 1732, 2000. Announced at DCC 1999.
42. Y. Lifshits. Processing compressed texts: A tractability border. In Proc. of the 18th symposium on Combinatorial Pattern Matching (CPM), pages 228-240, 2007.
43. V. Makinen, G. Navarro, and E. Ukkonen. Approximate matching of run-length compressed strings. In Proc. of the 12th Symposium On Combinatorial Pattern Matching (CPM), pages 1-13, 1999.
44. U. Manber. A text compression scheme that allows fast searching directly in the compressed file. In Proc of the 5th Symposium On Combinatorial Pattern Matching (CPM), pages 31-49, 1994.
45. K. Mehlhorn. Nearly optimal binary search trees. Acta Informatica, 5:287-295, 1975.
46. J. I. Munro and V. Raman. Succinct representation of balanced parentheses and static trees. SIAM Journal on Computing, 31(3):762-776, 2001. (Pubitemid 34750554)
47. J. I. Munro and S. S. Rao. Succinct representations of functions. In International Colloquium on Automata, Languages and Programming (ICALP), pages 1006-1015, 2004.
48. G. Navarro. A guided tour to approximate string matching. ACM Comput. Surv., 33(1):31-88, 2001. (Pubitemid 33768480)
49. G. Navarro, T. Kida, M. Takeda, A. Shinohara, and S. Arikawa. Faster approximate string matching over compressed text. In Proc. of the 11th Data Compression Conference (DCC), pages 459-468, 2001. (Pubitemid 32491018)
50. C. G. Nevill-Manning and I. H. Witten. Identifying hierarchical strcture in sequences: A linear-time algorithm. J. Artif. Intell. Res. (JAIR), 7:67-82, 1997.
51. M. Patraşcu. private communication. 2009.
52. W. Rytter. Application of Lempel-Ziv factorization to the approximation of grammar-based compression. Theoretical Computer Science, 302(1-3):211- 222, 2003.
53. K. Sadakane and G. Navarro. Fully-Functional Succinct Trees. In Proc. ACM-SIAM SODA, pages 134-149, Jan. 2010.
54. P. Sellers. The theory and computation of evolutionary distances: Pattern recognition. J. Algorithms, 1(4):359-373, 1980.
55. Y. Shibata, T. Kida, S. Fukamachi, M. Takeda, A. Shinohara, T. Shinohara, and S. Arikawa. Byte Pair encoding: A text compression scheme that accelerates pattern matching. Technical Report DOI-TR-161, Department of Informatics, Kyushu University, 1999.
56. Y. Shibata, T. Kida, S. Fukamachi, M. Takeda, A. Shinohara, T. Shinohara, and S. Arikawa. Speeding up pattern matching by text compression. In Proc. of the 4th Italian Conference Algorithms and Complexity (CIAC), pages 306-315, 2000.
57. R. E. Tarjan. Data Structures and Network Algorithms. SIAM, 1983.
58. T. A. Welch. A technique for high-performance data compression. IEEE Computer, 17(6):8-19, 1984.
59. 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, 46(3):755-754, 2000.
60. J. Ziv and A. Lempel. On the complexity of finite sequences. IEEE Transactions on Information Theory, 22(1):75-81, 1976.
61. J. Ziv and A. Lempel. A universal algorithm for sequential data compression. IEEE Transactions on Information Theory, 23(3):337-343, 1977.