Skip to main content
SpringerLink
Log in

A Linear Time Lower Bound on McCreight and General Updating Algorithms for Suffix Trees

  • Published:
Algorithmica Aims and scope Submit manuscript

Abstract

Suffix trees are the fundamental data structure of combinatorial pattern matching on words. Suffix trees have been used in order to give optimal solutions to a great variety of problems on static words, but for practical situations, such as in a text editor, where the incremental changes of the text make dynamic updating of the corresponding suffix trees necessary, this data structure alone has not been used with success. We prove that, for dynamic modifications of order O(1) of words of length n, any suffix tree updating algorithm, such as the ones proposed by McCreight, requires O(n) worst-case running time, as for the full reconstruction of the suffix tree. Consequently, we argue that this data structure alone is not appropriate for the solution of combinatorial problems on words that change dynamically.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Apostolico. The Myriad Virtues of Subword Trees. In A. Apostolico and Z. Galil, editors, Combinatorial Algorithms on Words, pages 85–96. Volume F12 of NATO ASI Series. Springer-Verlag, New York, 1985.

  2. A. Apostolico F. P. Preparata (1983) ArticleTitleOptimal Off-Line Detection of Repetitions in a String Theoretical Computer Science 22 297–315 Occurrence Handle0497.68052 Occurrence Handle10.1016/0304-3975(83)90109-3 Occurrence Handle693062

    Article  MATH  MathSciNet  Google Scholar 

  3. M. Ayala-Rincón and P. D. Conejo. A Linear Time Lower Bound on Updating Algorithms for Suffix Trees. In String Processing and Information Retrieval: A South American Symposium, pages 1–6, September 1998. Santa Cruz de La Sierra, Bolivia.

  4. P. D. Conejo. Limite Inferior para Algoritmos de Atualiza\ção de Árvores de Sufixos. Master’s thesis, Departamento de Matemática, Universidade de Brasília, 70910-900 Brasília, Brazil, November 1997. In Portuguese.

  5. M. Crochemore (1981) ArticleTitleAn Optimal Algorithm for Computing the Repetitions in a Word nformation Processing Letters 12 244–250 Occurrence Handle0467.68075 Occurrence Handle10.1016/0020-0190(81)90024-7 Occurrence Handle632873

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Farach. Optimal Suffix Tree Construction with Large Alphabets. In Proceedings of the IEEE Symposium on Foundations of Computer Science, pages 137–143, April 1997.

  7. P. Ferragina and R. Grossi. Fast Incremental Text Editing. In Proceedings of the Sixth Annual ACM–SIAM Symposium on Discrete Algorithms, SODA 95, pages 531–540, 1995.

  8. R. Griegerich S. Kurtz (1997) ArticleTitleFrom Ukkonen to McCreight and Weiner: A Unifying View of Linear-Time Suffix Tree Construction Algorithmica 19 331–353 Occurrence Handle10.1007/PL00009177 Occurrence Handle1471306

    Article  MathSciNet  Google Scholar 

  9. G. Kucherov M. Rusinowitch (1997) ArticleTitleMatching a Set of Strings with Variable Length Don’t Cares Theoretical Computer Science 178 129–154 Occurrence Handle0901.68037 Occurrence Handle10.1016/S0304-3975(97)88195-9 Occurrence Handle1453847

    Article  MATH  MathSciNet  Google Scholar 

  10. U. Manber G. Myers (1993) ArticleTitleSuffix Arrays: A New Method for On-line String Searches SIAM Journal on Computers 22 935–948 Occurrence Handle0784.68027 Occurrence Handle10.1137/0222058 Occurrence Handle1237156

    Article  MATH  MathSciNet  Google Scholar 

  11. E. M. McCreight (1976) ArticleTitleA Space-Economical Suffix Tree Construction Algorithm Journal of the Association for Computing Machinery 23 262–272 Occurrence Handle0329.68042 Occurrence Handle413594

    MATH  MathSciNet  Google Scholar 

  12. E. Ukkonen (1995) ArticleTitleOn-Line Construction of Suffix-Trees Algorithmica 14 249–260 Occurrence Handle0831.68027 Occurrence Handle10.1007/BF01206331 Occurrence Handle1343552

    Article  MATH  MathSciNet  Google Scholar 

  13. P. Weiner. Linear Pattern Matching Algorithms. In Proceedings of the IEEE 14th Annual Symposium on Switching and Automata Theory, pages 1–11, 1973.

Download references

Author information

Authors and Affiliations

  1. Departamento de Ciências Exatas, Universidade do Oeste de Santa Catarina, 89809 000 Chapecó, Brazil

    Mauricio Ayala-Rincón & Paulo D. Conejo

Authors
  1. Mauricio Ayala-Rincón
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paulo D. Conejo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Mauricio Ayala-Rincón or Paulo D. Conejo.

Additional information

Communicated by F. P. Preparata

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ayala-Rincón, M., Conejo, P. A Linear Time Lower Bound on McCreight and General Updating Algorithms for Suffix Trees. Algorithmica 37, 233–241 (2003). https://doi.org/10.1007/s00453-003-1034-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00453-003-1034-5

Search

Navigation