The Property Suffix Tree with Dynamic Properties

  • Tsvi Kopelowitz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6129)


Recently there has been much interest in the Property Indexing Problem ([1],[7],[8]), where one is interested to preprocess a text T of size n over alphabet Σ (which we assume is of constant size), and a set of intervals π over the text positions, such that give a query pattern P of size m we can report all of the occurrences of P in T which are completely contained within some interval from π. This type of matching is extremely helpful in scenarios in molecular biology where it has long been a practice to consider special areas in the genome by their structure.

The work done so far has focused on the static version of this problem where the intervals are given a-priori and never changed. This paper is the first to focus on several dynamic settings of π including an incremental version where new intervals are inserted into π, decremental version where intervals are deleted from π, fully dynamic version where intervals may be inserted or deleted to or from π, or batched insertions where a set of intervals is inserted into π. In particular, the batched version provides us with a new (optimal) algorithm for the static case.


Pattern Match Priority Queue Maximal Extent Text Location Property Match 
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.


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  1. 1.
    Amir, A., Chencinski, E., Iliopoulos, C.S., Kopelowitz, T., Zhang, H.: Property matching and weighted matching. Theor. Comput. Sci. 395, 298–310 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Boyer, R.S., Moore, J.S.: A fast string searching algorithm. Comm. ACM 20, 762–772 (1977)CrossRefGoogle Scholar
  3. 3.
    Cole, R., Gottlieb, L., Lewenstein, M.: Dictionary matching and indexing with errors and don’t cares. In: Proc. 36th annual ACM Symposium on the Theory of Computing (STOC), pp. 91–100. ACM Press, New York (2004)Google Scholar
  4. 4.
    Farach, M., Muthukrishnan, S.: Perfect Hashing for Strings: Formalization and Algorithms. In: Proc. 7th Combinatorial Pattern Matching Conference, pp. 130–140 (1996)Google Scholar
  5. 5.
    Ferragina, P., Grossi, R.: Fast incremental text editing. In: Proc. 7th ACM-SIAM Symposium on Discrete Algorithms, pp. 531–540 (1995)Google Scholar
  6. 6.
    Gu, M., Farach, M., Beigel, R.: An efficient algorithm for dynamic text indexing. In: Proc. 5th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 697–704 (1994)Google Scholar
  7. 7.
    Iliopoulos, C.S., Rahman, M.S.: Faster index for property matching. Inf. Process. Lett. 105(6), 218–223 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Juan, M.T., Liu, J.J., Wang, Y.L.: Errata for “Faster index for property matching“. Inf. Process. Lett. 109(18), 1027–1029 (2009)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Jurka, J.: Origin and Evolution of Alu Repetitive Elements. In: The Impact of Short Interspersed Elements (SINEs) on the Host Genome, pp. 25–41 (1995)Google Scholar
  10. 10.
    Jurka, J.: Human Repetitive Elements. In: Molecular Biology and Biotechnology, pp. 438–441 (1995)Google Scholar
  11. 11.
    Kärkkäinen, J., Sanders, P.: Simple linear work suffix array construction. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 943–955. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Kopelwoitz, T., Lewenstein, M.: Dynamic Weighted Ancestors. In: Proc. 18th Annual ACM-SIAM Symposium on Discrete Algorithms(SODA), pp. 565–574 (2003)Google Scholar
  13. 13.
    Knuth, D.E., Morris, J.H., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comp. 6, 323–350 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    McCreight, E.M.: A space-economical suffix tree construction algorithm. J. of the ACM 23, 262–272 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Sahinalp, S.C., Vishkin, U.: Efficient approximate and dynamic matching of patterns using a labeling paradigm. In: Proc. 37th FOCS, pp. 320–328 (1996)Google Scholar
  16. 16.
    Ukkonen, E.: On-line construction of suffix trees. Algorithmica 14, 249–260 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    van Emde Boas, P.: Preserving Order in a Forest in Less Than Logarithmic Time and Linear Space. Inf. Process. Letters 6(3), 80–82 (1977)zbMATHCrossRefGoogle Scholar
  18. 18.
    Weiner, P.: Linear pattern matching algorithm. In: Proc. 14th IEEE Symposium on Switching and Automata Theory, pp. 1–11 (1973)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tsvi Kopelowitz
    • 1
  1. 1.Department of Computer ScienceBar-Ilan UniversityRamat-GanIsrael

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