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Optimal parallel algorithms for periods, palindromes and squares

Extended abstract
  • Alberto Apostolico
  • Dany Breslauer
  • Zvi Galil
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 623)

Keywords

Parallel Algorithm Arithmetic Progression String Match Input String Stage Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Apostolico, A. (1991), Optimal parallel detection of squares in strings, CSTR-91-026, Purdue and Algorithmica, in press.Google Scholar
  2. [2]
    Apostolico, A. and Breslauer D. (1991), An optimal O(loglogn) time parallel algorithm for detecting all repetitions in a string, In preparation.Google Scholar
  3. [3]
    Apostolico, A. and Preparata, F. P. (1983), Optimal off-line detection of repetitions in a string, Theoretical Computer Science 22, 297–315.CrossRefGoogle Scholar
  4. [4]
    Beame, P., and Hastad, J. (1989), Optimal Bound for Decision Problems on the CRCW PRAM, Journal of ACM 36:3, 643–670.CrossRefGoogle Scholar
  5. [5]
    Brent, R. P. (1974), The parallel evaluation of general arithmetic expressions, J. ACM 81, 201–206.CrossRefGoogle Scholar
  6. [6]
    Breslauer, D. and Galil, Z. (1990), An optimal O(log logn) parallel string matching algorithm, SIAM J. Comput. 19:6, 1051–1058.CrossRefGoogle Scholar
  7. [7]
    Breslauer, D. and Galil, Z. (1991), A lower bound for parallel string matching, Proc. 23rd ACM Symp. on Theory of Computation, 439–443.Google Scholar
  8. [8]
    Breslauer, D. and Galil Z. (1991), Finding all the periods and initial palindromes of a string in parallel, manuscript.Google Scholar
  9. [9]
    Crochemore, M. (1981), An optimal algorithm for computing the repetitions in a word, Information Processing Letters 12:5, 244–250.Google Scholar
  10. [10]
    Crochemore, M. (1986), Transducer and repetitions, Theoretical Computer Science 45, 63–86.CrossRefGoogle Scholar
  11. [11]
    Crochemore, M. and Rytter, W. (1991), Usefulness of the Karp-Miller-Rosenberg algorithm in parallel computations on strings and arrays, Theoretical Computer Science 88, 59–82.CrossRefGoogle Scholar
  12. [12]
    Crochemore, M. and Rytter, W. (1991), Efficient Parallel Algorithms to Test Square-freeness and Factorize Strings, Information Processing Letters 38, 57–60.Google Scholar
  13. [13]
    Fich, F. E., Ragde, R. L., and Wigderson, A. (1984), Relations between concurrent-write models of parallel computation, Proc. 3rd ACM Symp. on Principles of Distributed Computing, 179–189.Google Scholar
  14. [14]
    Fischer, M. J. and Paterson, M. S. (1974), String-Matching and other products, SIAM-AMS proceedings, Vol 7, 113–125.Google Scholar
  15. [15]
    Knuth, D. E., Morris, J. H. and Pratt, V. R. (1977), Fast pattern matching in strings, SIAM J. Comput. 6, 322–350.CrossRefGoogle Scholar
  16. [16]
    Lyndon, R. C. and Schutzenberger, M. P. (1962), The equation a M — b N c P in a free group, Michigan Math. J. 9, 289–298.CrossRefGoogle Scholar
  17. [17]
    Main, G. M. and Lorentz, R. J. (1984), An O(n log n) algorithm for finding all repetitions in a string, Journal of Algorithms 5, 422–432.CrossRefGoogle Scholar
  18. [18]
    Main, G. M. and Lorentz, R. J. (1985), Linear time recognition of squarefree strings, in Combinatorial Algorithms on Words, Edited by A. Apostolico and Z. Galil, 271–278.Google Scholar
  19. [19]
    Thue, A. (1906), Über unendliche Zeichenreihen, Norske Vid. Selse. Skr. Mat. Nat Kl. (Cristiania), Nr. 7, 1–22.Google Scholar
  20. [20]
    Thue, A. (1912), Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen, Norske Vid. Selsk Skr. Mat. Nat. Kl. (Cristiania), Nr. 1, 1–67.Google Scholar
  21. [21]
    Vishkin, U. (1985), Optimal parallel pattern matching in strings, Information and Control 67, 91–113.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Alberto Apostolico
    • 1
  • Dany Breslauer
    • 2
  • Zvi Galil
    • 2
    • 3
  1. 1.Purdue University and Università di PadovaItaly
  2. 2.Columbia UniversityUSA
  3. 3.Tel-Aviv UniversityIsrael

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