Skip to main content

Optimal parallel algorithms for periods, palindromes and squares

Extended abstract

  • Conference paper
  • First Online:
Automata, Languages and Programming (ICALP 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 623))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Apostolico, A. (1991), Optimal parallel detection of squares in strings, CSTR-91-026, Purdue and Algorithmica, in press.

    Google Scholar 

  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. Apostolico, A. and Preparata, F. P. (1983), Optimal off-line detection of repetitions in a string, Theoretical Computer Science 22, 297–315.

    Article  Google Scholar 

  4. Beame, P., and Hastad, J. (1989), Optimal Bound for Decision Problems on the CRCW PRAM, Journal of ACM 36:3, 643–670.

    Article  Google Scholar 

  5. Brent, R. P. (1974), The parallel evaluation of general arithmetic expressions, J. ACM 81, 201–206.

    Article  Google Scholar 

  6. Breslauer, D. and Galil, Z. (1990), An optimal O(log logn) parallel string matching algorithm, SIAM J. Comput. 19:6, 1051–1058.

    Article  Google Scholar 

  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. Breslauer, D. and Galil Z. (1991), Finding all the periods and initial palindromes of a string in parallel, manuscript.

    Google Scholar 

  9. Crochemore, M. (1981), An optimal algorithm for computing the repetitions in a word, Information Processing Letters 12:5, 244–250.

    Google Scholar 

  10. Crochemore, M. (1986), Transducer and repetitions, Theoretical Computer Science 45, 63–86.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. Fischer, M. J. and Paterson, M. S. (1974), String-Matching and other products, SIAM-AMS proceedings, Vol 7, 113–125.

    Google Scholar 

  15. Knuth, D. E., Morris, J. H. and Pratt, V. R. (1977), Fast pattern matching in strings, SIAM J. Comput. 6, 322–350.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. Thue, A. (1906), Über unendliche Zeichenreihen, Norske Vid. Selse. Skr. Mat. Nat Kl. (Cristiania), Nr. 7, 1–22.

    Google Scholar 

  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. Vishkin, U. (1985), Optimal parallel pattern matching in strings, Information and Control 67, 91–113.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

W. Kuich

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Apostolico, A., Breslauer, D., Galil, Z. (1992). Optimal parallel algorithms for periods, palindromes and squares. In: Kuich, W. (eds) Automata, Languages and Programming. ICALP 1992. Lecture Notes in Computer Science, vol 623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55719-9_82

Download citation

  • DOI: https://doi.org/10.1007/3-540-55719-9_82

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55719-7

  • Online ISBN: 978-3-540-47278-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics