Skip to main content
SpringerLink
Log in

Saving comparisons in the Crochemore-Perrin string matching algorithm

  • Conference paper
  • First Online:
Book cover Algorithms—ESA '93 (ESA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 726))

Included in the following conference series:

Abstract

Crochemore and Perrin discovered an elegant linear-time constant-space string matching algorithm that makes at most 2n−m symbol comparison. This paper shows how to modify their algorithm to use fewer comparisons.

Given any fixed ε>0, the new algorithm takes linear time, uses constant space and makes at most n+[1+ε/2(n−m)] symbol comparisons. If O(log m) space is available, then the algorithm makes at most n + [1/2(n − m)] symbol comparisons. The pattern preprocessing step also takes linear time and uses constant space.

These are the first string matching algorithms that make fewer than 2n & -m symbol comparisons and use sub-linear space.

Partially supported by the IBM Graduate Fellowship while studying at Columbia University in New York and by the European Research Consortium for Informatics and Mathematics postdoctoral fellowship while staying at the Centrum voor Wiskunde en Informatica in Amsterdam, The Netherlands. Part of this work was done while visiting at Università de L'Aquila, L'Aquila, Italy in summer 1991.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Apostolico and R. Giancarlo. The Boyer-Moore-Galil string searching strategies revisited. SIAM J. Comput., 15(1):98–105, 1986.

    Google Scholar 

  2. A. B. Borodin, M. J. Fischer, D. G. Kirkpatrick, N. A. Lynch, and M. Tompa. A time-space tradeoff for sorting on non-oblivious machines. In Proc. 20th IEEE Symp. on Foundations of Computer Science, pages 294–301, 1979.

    Google Scholar 

  3. R.S. Boyer and J.S. Moore. A fast string searching algorithm. Comm. of the ACM, 20:762–772, 1977.

    Google Scholar 

  4. D. Breslauer and Z. Galil. Efficient Comparison Based String Matching. J. Complexity, 1993. To appear.

    Google Scholar 

  5. Y. Cesari and M. Vincent. Une caractérisation des mots periodiques. C.R. Acad. Sci. Paris, 286(A):1175–1177, 1978.

    Google Scholar 

  6. R. Cole. Tight bounds on the complexity of the Boyer-Moore pattern matching algorithm. In Proc. 2nd ACM-SIAM Symp. on Discrete Algorithms, pages 224–233, 1991.

    Google Scholar 

  7. R. Cole and R. Hariharan. Tighter Bounds on The Exact Complexity of String Matching. In Proc. 33rd IEEE Symp. on Foundations of Computer Science, pages 600–609, 1992.

    Google Scholar 

  8. R. Cole, R. Hariharan, M.S. Paterson, and U. Zwick. Which patterns are hard to find. In Proc. 2nd Israeli Symp. on Theoretical Computer Science, pages 59–68, 1993.

    Google Scholar 

  9. L. Colussi. Correctness and efficiency of string matching algorithms. Inform. and Control, 95:225–251, 1991.

    Google Scholar 

  10. M. Crochemore. String-matching on ordered alphabets. Theoret. Comput. Sci., 92:33–47, 1992.

    Google Scholar 

  11. M. Crochemore and D. Perrin. Two-way string-matching. J. Assoc. Comput. Mach., 38(3):651–675, 1991.

    Google Scholar 

  12. M. Crochemore and W. Rytter. Periodic Prefixes in Texts. In R. Capocelli, A. De Santis, and U. Vaccaro, editors, Proc. of the Sequences '91 Workshop: “Sequences II: Methods in Communication, Security and Computer Science”, pages 153–165. Springer-Verlag, 1993.

    Google Scholar 

  13. Z. Galil and R. Giancarlo. On the exact complexity of string matching: lower bounds. SIAM J. Comput., 20(6):1008–1020, 1991.

    Google Scholar 

  14. Z. Galil and R. Giancarlo. The exact complexity of string matching: upper bounds. SIAM J. Comput., 21(3):407–437, 1992.

    Google Scholar 

  15. Z. Galil and J. Seiferas. Saving space in fast string-matching. SIAM J. Comput., 2:417–438, 1980.

    Google Scholar 

  16. Z. Galil and J. Seiferas. Linear-time string-matching using only a fixed number of local storage locations. Theoret. Comput. Sci., 13:331–336, 1981.

    Google Scholar 

  17. Z. Galil and J. Seiferas. Time-space-optimal string matching. J. Comput. System Sci., 26:280–294, 1983.

    Google Scholar 

  18. L. Guibas and A. M. Odlyzko. Periods in strings. Journal of Combinatorial Theory, Series A, 30:19–42, 1981.

    Google Scholar 

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

    Google Scholar 

  20. M. Lothaire. Combinatorics on Words. Addison-Wesley, Reading, MA., U.S.A., 1983.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut National de Recherche en Informatique et en Automatique, B.P. 105, 78153, Le Chesnay Cedex, France

    Dany Breslauer

Authors
  1. Dany Breslauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Thomas Lengauer

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Breslauer, D. (1993). Saving comparisons in the Crochemore-Perrin string matching algorithm. In: Lengauer, T. (eds) Algorithms—ESA '93. ESA 1993. Lecture Notes in Computer Science, vol 726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57273-2_44

Download citation

  • DOI: https://doi.org/10.1007/3-540-57273-2_44

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57273-2

  • Online ISBN: 978-3-540-48032-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation