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The suffix tree of a tree and minimizing sequential transducers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1075))

Abstract

This paper gives a linear-time algorithm for the construction of the suffix tree of a tree. The suffix tree of a tree is used to obtain an efficient algorithm for the minimization of sequential transducers.

Partially supported by the ESPRIT Basic Research Action Program of the EC under contract #7141 (ALCOM II).

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References

  1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, MA, 1974.

    Google Scholar 

  2. R.K. Ahuja, T.L. Magnanti, and J.B. Orlin. Network Flows. Prentice Hall, Englewood Cliffs, NJ, 1993.

    Google Scholar 

  3. R.K. Ahuja, K. Mehlhorn, J.B. Orlin, and R.E. Tarjan. Faster Algorithms for the Shortest Path Problem. J. Assoc. Comput. Mach., 37(2):213–223, 1990.

    Google Scholar 

  4. A. Amir, M. Farach, R.M. Idury, J.A. La Poutré, and A.A. Schäffer. Improved Dynamic Dictionary-Matching. In Proc. 4th ACM-SIAM Symp. on Discrete Algorithms, pages 392–401, 1993.

    Google Scholar 

  5. A. Apostolico. The Myriad Virtues of Subword Trees. In A. Apostolico and Z. Galil, editors, Combinatorial Algorithms on Words, volume 12 of NATO ASI Series F, pages 85–96. Springer-Verlag, Berlin, Germany, 1985.

    Google Scholar 

  6. O. Berkman and U. Vishkin. Finding Level-Ancestors in Trees. J. Comput. System Sci., 48:214–230, 1994.

    Google Scholar 

  7. M.T. Chen and J. Seiferas. Efficient and elegant subword-tree construction. In A. Apostolico and Z. Galil, editors, Combinatorial Algorithms on Words, volume 12 of NATO ASI Series F, pages 97–107. Springer-Verlag, Berlin, Germany, 1985.

    Google Scholar 

  8. R. Dial. Algorithm 360: Shortest path forest with topological ordering. Comm. of the ACM, 12:632–633, 1969.

    Google Scholar 

  9. R. Grossi and G.F. Italiano. Suffix Trees and their Applications in String Algorithms. Manuscript, 1995.

    Google Scholar 

  10. D. Harel and R.E. Tarjan. Fast algorithms for finding nearest common ancestors. SIAM J. Comput., 13:338–355, 1984.

    Article  Google Scholar 

  11. M. Harrison. Introduction to Formal Language Theory. Addison-Wesley, Reading, MA, U.S.A., 1978.

    Google Scholar 

  12. J.E. Hopcroft. An n log n algorithm for minimizing states in a finite automaton. In Z. Kohavi and A. Paz, editors, Theory of Machines and Computation, pages 189–196. Academic Press, New York, U.S.A., 1971.

    Google Scholar 

  13. S.R. Kosaraju. Fast Pattern Matching in Trees. In Proc. 30th IEEE Symp. on Foundations of Computer Science, pages 178–183, 1989.

    Google Scholar 

  14. E.M. McCreight. A space economical suffix tree construction algorithm. J. Assoc. Comput. Mach., 23:262–272, 1976.

    Google Scholar 

  15. M. Mohri. Minimization of Sequential Transducers. In Proc. 5th Symp. on Combinatorial Pattern Matching, number 807 in Lecture Notes in Computer Science, pages 151–163. Springer-Verlag, Berlin, Germany, 1994.

    Google Scholar 

  16. B. Schieber and U. Vishkin. On finding Lowest common ancestors: simplification and parallelization. SIAM J. Comput., 17(6):1253–1262, 1988.

    Article  Google Scholar 

  17. M. Thorup. An O(log log n) Priority Queue. Manuscript, 1995.

    Google Scholar 

  18. P. Weiner. Linear pattern matching algorithms. In Proc. 14th Symposium on Switching and Automata Theory, pages 1–11, 1973.

    Google Scholar 

  19. J. Westbrook. Fast Incremental Planarity Testing. In Proc. 19th International Colloquium on Automata, Languages, and Programming, number 623 in Lecture Notes in Computer Science, pages 342–353. Springer-Verlag, Berlin, Germany, 1992.

    Google Scholar 

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Dan Hirschberg Gene Myers

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© 1996 Springer-Verlag Berlin Heidelberg

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Breslauer, D. (1996). The suffix tree of a tree and minimizing sequential transducers. In: Hirschberg, D., Myers, G. (eds) Combinatorial Pattern Matching. CPM 1996. Lecture Notes in Computer Science, vol 1075. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61258-0_10

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  • DOI: https://doi.org/10.1007/3-540-61258-0_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61258-2

  • Online ISBN: 978-3-540-68390-2

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