A Simple Construction of Two-Dimensional Suffix Trees in Linear Time

(Extended Abstract)
  • Dong Kyue Kim
  • Joong Chae Na
  • Jeong Seop Sim
  • Kunsoo Park
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4580)

Abstract

The two-dimensional suffix tree of a matrix A is a compacted trie that represents all square submatrices of A. There exists a linear-time construction of two-dimensional suffix trees using the odd-even scheme. This algorithm has the drawback that the merging step is quite complicated. In this paper, we propose a new and simple algorithm to construct two-dimensional suffix trees in linear time by applying the skew scheme to square matrices. To do this, we present a simple algorithm to merge two Isuffix trees in linear time.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amir, A., Farach, M.: Two-dimensional dictionary matching. IPL 21, 233–239 (1992)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Apostolico, A.: The myriad virtues of subword trees. In: Apostolico, A., Galil, Z. (eds.) Combinatorial Algorithms on Words, pp. 85–95. Springer, Heidelberg (1985)Google Scholar
  3. 3.
    Chen, M.T., Seiferas, J.: Efficient and elegant subword tree construction. In: Apostolico, A., Galil, Z. (eds.) Combinatorial Algorithms on Words, F. NATO Advanced Science Institutes, vol. 12, pp. 97–107. Springer, Heidelberg (1985)Google Scholar
  4. 4.
    Cole, R., Hariharan, R.: Faster suffix tree construction with missing suffix links. In: Proc. of the 30th STOC, pp. 407–415 (2000)Google Scholar
  5. 5.
    Crochemore, M., Rytter, W.: Jewels of Stringology. World Scientific Publishing, Singapore (2002)Google Scholar
  6. 6.
    Farach, M.: Optimal suffix tree construction with large alphabets. In: Proc. of the 38th FOCS, pp. 137–143 (1997)Google Scholar
  7. 7.
    Farach, M., Muthukrishnan, S.: Optimal logarithmic time randomized suffix tree construction. In: Proc. of the 23rd ICALP, pp. 550–561 (1996)Google Scholar
  8. 8.
    Farach-Colton, M., Ferragina, P., Muthukrishnan, S.: On the sorting-complexity of suffix tree construction. J. ACM 47(6), 987–1011 (2000)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Giancarlo, R.: A generalization of the suffix tree to square matrices, with application. SIAM J. on Comp. 24(3), 520–562 (1995)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Giancarlo, R., Grossi, R.: On the construction of classes of suffix trees for square matrices: Algorithms and applications. Information and Computation 130(2), 151–182 (1996)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Giancarlo, R., Grossi, R.: Suffix tree data structures for matrices. In: Apostolico, A., Galil, Z. (eds.) Pattern Matching Algorithms, chapter 11, pp. 293–340. Oxford University Press, Oxford (1997)Google Scholar
  12. 12.
    Giancarlo, R., Guaiana, D.: On-line construction of two-dimensional suffix trees. Journal of Complexity 15(1), 72–127 (1999)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Gonnet, G.H.: Efficient searching of text and pictures. Technical Report OED-88-02, University of Waterloo (1988)Google Scholar
  14. 14.
    Gusfield, D.: Algorithms on Strings, Tree, and Sequences. Cambridge University Press, Cambridge (1997)Google Scholar
  15. 15.
    Harel, D., Tarjan, R.: Fast algorithms for finding nearest common ancestors. SIAM J. on Comp. 13(2), 338–355 (1984)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Hariharan, R.: Optimal parallel suffix tree construction. In: Proc. of the 26th FOCS, pp. 290–299 (1994)Google Scholar
  17. 17.
    Hon, W.K., Sadakane, K., Sung, W.K.: Breaking a time-and-space barrier in constructing full-text indices. In: Proc. of the 44th FOCS, pp. 251–260 (2003)Google Scholar
  18. 18.
    Kärkkäinen, J., Sanders, P., Burkhardt, S.: Linear work suffix array construction. J. ACM (in press)Google Scholar
  19. 19.
    Kim, D.K., Kim, Y.A., Park, K.: Generalizations of suffix arrays to multi-dimensional matrices. TCS 302(1-3), 401–416 (2003)MATHCrossRefGoogle Scholar
  20. 20.
    Kim, D.K., Park, K.: Linear-time construction of two-dimensional suffix trees. In: Proc. of the 26th ICALP, pp. 463–372 (1999)Google Scholar
  21. 21.
    Kim, D.K., Sim, J.S., Park, H., Park, K.: Constructing suffix arrays in linear time. J. Disc. Alg. 3(2-4), 126–142 (2005)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Ko, P., Aluru, S.: Space efficient linear time construction of suffix arrays. J. Disc. Alg. 3(2-4), 143–156 (2005)MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Manber, U., Myers, G.: Suffix arrays: A new method for on-line string searches. SIAM J. on Comp. 22(5), 935–948 (1993)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    McCreight, E.M.: A space-economical suffix tree construction algorithms. J. ACM 23(2), 262–272 (1976)MATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Na, J.C., Giancarlo, R., Park, K.: O(n2logn) time on-line construction of two-dimensional suffix trees. In: Proc. of the 11th COCOON, pp. 273–282 (2005)Google Scholar
  26. 26.
    Sahinalp, S.C., Vishkin, U.: Symmetry breaking for suffix tree construction. In: Proc. of the 26th FOCS, pp. 300–309 (1994)Google Scholar
  27. 27.
    Schieber, B., Vishkin, U.: On finding lowest common ancestors: Simplification and parallelization. SIAM J. on Comp. 17(6), 1253–1262 (1988)MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Ukkonen, E.: On-line construction of suffix trees. Algorithmica 14(3), 249–260 (1995)MATHCrossRefMathSciNetGoogle Scholar
  29. 29.
    Weiner, P.: Linear pattern matching algorithms. In: Proc. of the 14th IEEE Symp. on Switching and Automata Theory, pp. 1–11 (1973)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Dong Kyue Kim
    • 1
  • Joong Chae Na
    • 2
  • Jeong Seop Sim
    • 3
  • Kunsoo Park
    • 4
  1. 1.Division of Electronics and Computer Engineering, Hanyang UniversityKorea
  2. 2.Department of Advanced Technology Fusion, Konkuk UniversityKorea
  3. 3.School of Computer Science and Engineering, Inha UniversityKorea
  4. 4.School of Computer Science and Engineering, Seoul National UniversityKorea

Personalised recommendations