On the complexity of determining the period of a string

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1848, Issue , 2000, Pages 412-422

  Czumaj, Artur ^a   Gaşieniec, Leszek ^b  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; COMPUTER SCIENCE; COMPUTERS;

ALGORITHM COMPUTING; AVERAGE CASE; COMBINATORIAL PROBLEM; DETERMINISTIC ALGORITHMS; INPUT STRING; TIGHT BOUND; WORST-CASE COMPLEXITY;

PATTERN MATCHING;

EID: 84937432920     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45123-4_34     Document Type: Conference Paper

References (45)

1. A. V. Aho. Algorithms for finding patterns in strings. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity, chapter 5, pages 257-300. Elsevier Science, Amsterdam, 1990
2. A. Amir and G. Benson. Two-dimensional periodicity in rectangular arrays. SIAM Journal on Computing, 27(1):90-106, February 1998
3. A. Amir, G. Benson, and M. Farach. Alphabet independent two dimensional matching. In Proceedings of the 24th Annual ACM Symposium on Theory of Computing, pages 59-68, Victoria, British Columbia, Canada, May 4-6, 1992. ACM Press, New York, NY
4. A. Amir, G. Benson, and M. Farach. An alphabet independent approach to two-dimensional pattern matching. SIAM Journal on Computing, 23(2):313-323, April 1994
5. A. Apostolico and M. Crochemore. Optimal canonization of all substrings of a string. Information and Computation, 95(1):76-95, November 1991
6. A. Apostolico and Z. Galil, editors. Pattern Matching Algorithms. Oxford University Press, New York, NY, 1997
7. A. Apostolico and R. Giancarlo. The Boyer-Moore-Galil string searching strategies revisited. SIAM Journal on Computing, 15(1):98-105, February 1986
8. R. S. Boyer and J. S. Moore. A fast string searching algorithm. Communications of the ACM, 20:762-772, 1977
9. D. Breslauer, L. Colussi, and L. Toniolo. Tight comparison bounds for the string prefixmatching problem. Information Processing Letters, 47(1):51-57, August 1993
10. D. Breslauer, L. Colussi, and L. Toniolo. On the comparison complexity of the string prefixmatching problem. Journal of Algorithms, 29(1):18-67, October 1998
11. D. Breslauer and Z. Galil. An optimal O(log log n) time parallel string matching algorithm. SIAM Journal on Computing, 19(6):1051-1058, December 1990
12. D. Breslauer and Z. Galil. A lower bound for parallel string matching. SIAM Journal on Computing, 21(5):856-862, October 1992. A preliminary version appears in Proceedings of the 23rd Annual ACM Symposium on Theory of Computing, pages 439-443, New Orleans, Louisiana, May 6-8, 1991. ACM Press, New York, NY
13. D. Breslauer and Z. Galil. Efficient comparison based string matching. Journal of Complexity, 9(3):339-365, September 1993
14. R. Cole. Tight bounds on the complexity of the Boyer-Moore string matching algorithm. SIAM Journal on Computing, 23(5):1075-1091, October 1994
15. R. Cole, M. Crochemore, Z. Galil, L. Gaşieniec, R. Hariharan, S. Muthukrishnan, K. Park, and W. Rytter. Optimally fast parallel algorithms for preprocessing and pattern matching in one and two dimensions. In Proceedings of the 34th IEEE Symposium on Foundations of Computer Science, pages 248-258, Palo Alto, CA, November 3-5, 1993. IEEE Computer Society Press, Los Alamitos, CA
16. R. Cole and R. Hariharan. Tighter upper bounds on the exact complexity of string matching. SIAM Journal on Computing, 26(3):803-856, June 1997
17. R. Cole, R. Hariharan, M. Paterson, and U. Zwick. Tighter lower bounds on the exact complexity of string matching. SIAM Journal on Computing, 24(1):30-45, February 1995
18. L. Colussi. Correctness and efficiency of pattern matching algorithms. Information and Computation, 95(2):225-251, December 1991
19. L. Colussi, Z. Galil, and R. Giancarlo. On the exact complexity of string matching. In Proceedings of the 22nd Annual ACM Symposium on Theory of Computing, pages 135-144, Baltimore, MD, May 14-16, 1990. ACM Press, New York, NY
20. M. Crochemore. Off-line serial exact string searching. In A. Apostolico and Z. Galil, editors, Pattern Matching Algorithms, chapter I, pages 1-53. Oxford University Press, New York, NY, 1997
21. M. Crochemore. String-matching on ordered alphabets. Theoretical Computer Science, 92(1):33-47, January 1992
22. M. Crochemore, A. Czumaj, L. Gaşieniec, S. Jarominek, T. Lecroq, W. Plandowski, and W. Rytter. Speeding up two string-matching algorithms. Algorithmica, 12(4/5):247-267, October 1994
23. M. Crochemore, Z. Galil, L. Gaşieniec, K. Park, and W. Rytter. Constant-time randomized parallel string matching. SIAM Journal on Computing, 26(4):950-960, August 1997
24. M. Crochemore, L. Gaşieniec, W. Plandowski, and W. Rytter. Two-dimensional pattern matching in linear time and small space. In Proceedings of the 12th Annual Symposium on Theoretical Aspects of Computer Science, volume 900 of LectureNotes in Computer Science, pages 181-192, Munich, Germany, March 2-4, 1995. Springer-Verlag, Berlin
25. M. Crochemore and D. Perrin. Two-way string-matching. Journal of the ACM, 38(3):651-675, July 1991
26. M. Crochemore and W. Rytter. Text Algorithms. Oxford University Press, New York, NY, 1994
27. A. Czumaj, Z. Galil, L. Gaşieniec, K. Park, and W. Plandowski. Work-time-optimal parallel algorithms for string problems. In Proceedings of the 27th Annual ACM Symposium on Theory of Computing, pages 713-722, Las Vegas, NV, May 29-June 1, 1995. ACM Press, New York, NY
28. Z. Galil. Real-time algorithms for string-matching and palindrome recognition. In Proceedings of the 8th Annual ACM Symposium on Theory of Computing, pages 161-173, Hershey, PA, May 3-5, 1976. ACM Press, New York, NY
29. Z. Galil. On improving the worst case running time of the Boyer-Moore string matching algorithm. Communications of the ACM, 22(9):505-508, September 1979
30. Z. Galil. Optimal parallel algorithms for string matching. Information and Computation, 67(1-3):144-157, 1985
31. Z. Galil and R. Giancarlo. On the exact complexity of string matching: Lower bounds. SIAM Journal on Computing, 20(6):1008-1020, December 1991
32. Z. Galil and K. Park. Alphabet-independent two-dimensional witness computation. SIAM Journal on Computing, 25(5):907-935, October 1996
33. Z. Galil and J. Seiferas. Time-space-optimal string matching. Journal of Computer and System Sciences, 26(3):280-294, June 1983
34. L. Gaşieniec, W. Plandowski, and W. Rytter. Constant-space string matching with smaller number of comparisons: Sequential sampling. In Z. Galil and E. Ukkonen, editors, Proceedings of the 6th Symposiumon Combinatorial PatternMatching, volume 937 of LectureNotes in Computer Science, pages 78-89, Espoo, Finland, July 5-7, 1995. Springer-Verlag, Berlin
35. L. Gaşieniec, W. Plandowski, and W. Rytter. The zooming method: a recursive approach to time-space efficient string-matching. Theoretical Computer Science, 147(1-2):19-30, August 1995
36. D. Gusfield. Algorithms on Strings, Trees and Sequences. Cambridge University Press, New York, NY, 1997
37. D. E. Knuth, J. H. Morris, and V. R. Pratt. Fast pattern matching in strings. SIAM Journal on Computing, 6(2):323-350, June 1977
38. M. Lothaire. Combinatorics on Words. Addison-Wesley, Reading, MA, 1983
39. M. Lothaire. Algebraic Combinatorics on Words. Addison-Wesley, Reading, MA, 1999
40. R.C Lyndon and M.P. Schutzenberger. The equation am = bncp in a free group, Michigan Math. J., 9: 289-298, 1962
41. R. L. Rivest. On the worst case behavior of string searching algorithms. SIAM Journal on Computing, 6(4):669-674, December 1977
42. W. Rytter. A correct preprocessing algorithm for Boyer-Moore string-searching. SIAM Journal on Computing, 9(3):509-512, August 1980
43. U. Vishkin. Optimal parallel pattern matching in strings. Information and Computation, 67(1-3):91-113, October 1985
44. U. Vishkin. Deterministic sampling-a new technique for fast pattern matching. SIAM Journal on Computing, 20(1):22-40, February 1991
45. A. C. Yao. The complexity of pattern matching for a random string. SIAM Journal on Computing, 8(3):368-387, August 1979