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Succinct Non-overlapping Indexing

  • Arnab GangulyEmail author
  • Rahul Shah
  • Sharma V. Thankachan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9133)

Abstract

Given a text \(\mathsf {T}\) having \(n\) characters, we consider the non-overlapping indexing problem defined as follows: pre-process \(\mathsf {T}\) into a data-structure, such that whenever a pattern \(P\) comes as input, we can report a maximal set of non-overlapping occurrences of \(P\) in \(\mathsf {T}\). The best known solution for this problem takes linear space, in which a suffix tree of \(\mathsf {T}\) is augmented with \(O(n)\)-word data structures. A query \(P\) can be answered in optimal \(O(|P|+\mathsf {nocc})\) time, where \(\mathsf {nocc}\) is the output size [Cohen and Porat, ISAAC 2009]. We present the following new result: let \(\mathsf {CSA}\) (not necessarily a compressed suffix array) be an index of \(\mathsf {T}\) that can compute (i) the suffix range of \(P\) in \(\mathsf {search}(P)\) time, and (ii) a suffix array or an inverse suffix array value in \(\mathsf {t_{SA}}\) time; then by using \(\mathsf {CSA}\) alone, we can answer a query \(P\) in \(O(\mathsf {search}(P)+ \mathsf {nocc}\cdot \mathsf {t_{SA}})\) time. Additionally, we present an improved result for a generalized version of this problem called range non-overlapping indexing.

Keywords

Query Time Suffix Tree Suffix Array Output Size Short Pattern 
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.

References

  1. 1.
    Abouelhoda, M.I., Kurtz, S., Ohlebusch, E.: Replacing suffix trees with enhanced suffix arrays. J. Discret. Algorithms 2(1), 53–86 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Alstrup, S., Brodal, G.S., Rauhe, T.: New data structures for orthogonal range searching. In: 41st Annual Symposium on Foundations of Computer Science, FOCS 2000, 12–14 November 2000, Redondo Beach, California, USA, pp. 198–207 (2000)Google Scholar
  3. 3.
    Alstrup, S., Brodal, G.S., Rauhe, T.: Optimal static range reporting in one dimension. In: Proceedings on 33rd Annual ACM Symposium on Theory of Computing, 6–8 July 2001, Heraklion, Crete, Greece, pp. 476–482 (2001)Google Scholar
  4. 4.
    Belazzougui, D., Navarro, G.: Alphabet-independent compressed text indexing. ACM Trans. Algorithms 10(4), 23 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Boyer, R.S., Moore, J.S.: A fast string searching algorithm. Commun. ACM 20(10), 762–772 (1977)zbMATHCrossRefGoogle Scholar
  6. 6.
    Cohen, H., Porat, E.: Range non-overlapping indexing. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 1044–1053. Springer, Heidelberg (2009) CrossRefGoogle Scholar
  7. 7.
    Crochemore, M., Iliopoulos, C.S., Kubica, M., Rahman, M.S., Walen, T.: Improved algorithms for the range next value problem and applications. In: STACS 2008, Proceeding of the 25th Annual Symposium on Theoretical Aspects of Computer Science, Bordeaux, France, 21–23 February 2008, pp. 205–216 (2008)Google Scholar
  8. 8.
    Ferragina, P., Manzini, G.: Indexing compressed text. J. ACM 52(4), 552–581 (2005)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Grossi, R., Vitter, J.S.: Compressed suffix arrays and suffix trees with applications to text indexing and string matching (extended abstract). In: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, 21–23 May 2000, Portland, OR, USA, pp. 397–40 (2000)Google Scholar
  10. 10.
    Gusfield, D.: Algorithms on Strings, Trees, and Sequences : Computer Science and Computational Biology. Cambridge University Press, New York (1997) zbMATHCrossRefGoogle Scholar
  11. 11.
    Hon, W., Shah, R., Thankachan, S.V., Vitter, J.S.: On position restricted substring searching in succinct space. J. Discret. Algorithms 17, 109–114 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    Karp, R.M., Rabin, M.O.: Efficient randomized pattern-matching algorithms. IBM J. Res. Dev. 31(2), 249–260 (1987)zbMATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    Keller, O., Kopelowitz, T., Lewenstein, M.: Range non-overlapping indexing and successive list indexing. In: Dehne, F., Sack, J.-R., Zeh, N. (eds.) WADS 2007. LNCS, vol. 4619, pp. 625–636. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  14. 14.
    Knuth, D.E., Jr., J.H.M., Pratt, V.R.: Fast pattern matching in strings. SIAM J. Comput. 6(2), 323–350 (1977)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Mäkinen, V., Navarro, G.: Position-restricted substring searching. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 703–714. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  16. 16.
    Manber, U., Myers, E.W.: Suffix arrays: a new method for on-line string searches. SIAM J. Comput. 22, 935–948 (1993)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Navarro, G., Mäkinen, V.: Compressed full-text indexes. ACM Comput. Surv., vol. 39(1) (2007)Google Scholar
  18. 18.
    Nekrich, Y., Navarro, G.: Sorted range reporting. In: Fomin, F.V., Kaski, P. (eds.) SWAT 2012. LNCS, vol. 7357, pp. 271–282. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  19. 19.
    Ukkonen, E.: On-line construction of suffix trees. Algorithmica 14(3), 249–260 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Weiner, P.: Linear pattern matching algorithms. In: 14th Annual Symposium on Switching and Automata Theory, Iowa City, Iowa, USA, 15–17 October 1973, pp. 1–11 (1973)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Arnab Ganguly
    • 1
    Email author
  • Rahul Shah
    • 1
  • Sharma V. Thankachan
    • 2
  1. 1.School of Electrical Engineering and Computer ScienceLouisiana State UniversityBaton RougeUSA
  2. 2.School of Computational Science and EngineeringGeorgia Institute of TechnologyAtlantaUSA

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