Advertisement

Constructing the Suffix Tree of a Tree with a Large Alphabet

  • Tetsuo Shibuya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1741)

Abstract

The problem of constructing the suffix tree of a common suffix tree (CS-tree) is a generalization of the problem of constructing the suffix tree of a string. It has many applications, such as in minimizing the size of sequential transducers and in tree pattern matching. The best-known algorithm for this problem is Breslauer’s O(n log |∑|) time algorithm where n is the size of the CS-tree and |∑| is the alphabet size, which requires O(n log n) time if |∑| is large. We improve this bound by giving an O(n log n) algorithm for integer alphabets. For trees called shallow k-ary trees, we give an optimal linear time algorithm. We also describe a new data structure, the Bsuffix tree, which enables efficient query for patterns of completely balanced k-ary trees from a k-ary tree or forest. We also propose an optimal O(n) algorithm for constructing the Bsuffix tree for integer alphabets.

Keywords

Binary Number Edge Label Suffix Tree Large Alphabet Balance Binary Tree 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Apostolico and Z. Galil, eds., “Pattern Matching Algorithms”, Oxford University Press, New York, 1997.Google Scholar
  2. 2.
    D. Breslauer, “The Suffix Tree of a Tree and Minimizing Sequential Transducers,” J. Theoretical Computer Science, Vol. 191, 1998, pp. 131–144.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    M. T. Chen and J. Seiferas, “Efficient and Elegant Subword Tree Construction,” A. Apostolico and Z. Galil, eds., Combinatorial Algorithms on Words, Chapter 12, NATO ASI Series F: Computer and System Sciences, 1985, pp. 97–107.Google Scholar
  4. 4.
    R. Cole, R. Hariharan and P. Indyk, “Tree Pattern Matching and Subset Matching in Deterministic O(n log3 n)-time,” Proc. 4th Symposium on Discrete Mathematics (SODA’ 99), 1999, pp. 245–254.Google Scholar
  5. 5.
    M. Farach, “Optimal Suffix Tree Construction with Large Alphabets,” Proc. 38th IEEE Symp. Foundations of Computer Science (FOCS’ 97), 1997, pp. 137–143.Google Scholar
  6. 6.
    M. Farach and S. Muthukrishnan, “Optimal Logarithmic Time Randomized Suffix Tree Construction,” Proc. 23rd International Colloquium on Automata Languages and Programming (ICALP’ 96), 1996, pp. 550–561.Google Scholar
  7. 7.
    R. Giancarlo, “The Suffix Tree of a Square Matrix, with Applications,” Proc. 4th Symposium on Discrete Mathematics (SODA’ 93), 1993, pp. 402–411.Google Scholar
  8. 8.
    D. Gusfield, “Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology,” Cambridge University Press, 1997.Google Scholar
  9. 9.
    D. Harel and R. R. Tarjan, “Fast Algorithms for Finding Nearest Common Ancestors,” SIAM J. Computing, Vol. 13, 1984, pp. 338–355.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    S. R. Kosaraju, “Efficient Tree Pattern Matching,” Proc. 30th IEEE Symp. Foundations of Computer Science (FOCS’ 89), 1989, pp. 178–183.Google Scholar
  11. 11.
    E. M. McCreight, “A Space-Economical Suffix Tree Construction Algorithm,” J. ACM, Vol. 23, 1976, pp. 262–272.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    E. Ukkonen, “On-Line Construction of Suffix-Trees,” Algorithmica, Vol. 14, 1995, pp. 249–60.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    P. Weiner, “Linear Pattern Matching Algorithms,” Proc. 14th Symposium on Switching and Automata Theory, 1973, pp. 1–11.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Tetsuo Shibuya
    • 1
  1. 1.IBM Tokyo Research LaboratoryYamato-shiJapan

Personalised recommendations