Advertisement

Computing the Minimum λ-Cover in Weighted Sequences

  • Hui Zhang
  • Qing Guo
  • Costas S. Iliopoulos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7389)

Abstract

Given a weighted sequence X of length n and an integer constant λ, the minimum λ-cover problem of weighted sequences is to find the sets of λ factors of X each of equal length such that the set covers X, and the length of each element in the set is minimum. By constructing the Equivalence Class Tree and iteratively computing the occurrences of a set of factors in weighted sequences, we tackle the problem in O(n 2) time for constant alphabet size.

Keywords

Weighted sequence the minimum λ-cover problem λ-combination Equivalence Class Tree 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Apostolico, A., Farach, M., Iliopoulos, C.S.: Optimal Superprimitivity Testing for Strings. Information Processing Letters 39, 17–20 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Breslauer, D.: An On-line String Superprimitivity Test. Information Processing Letters 44, 345–347 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Cole, R., Iliopoulos, C.S., Mohamed, M., Smith, W.F., Yang, L.: Computing the Minimum k-cover of a String. In: Proc. of the 2003 Prague Stringology Conference (PSC 2003), pp. 51–64 (2003)Google Scholar
  4. 4.
    Christodoulakis, M., Iliopoulos, C.S., Mouchard, L., Perdikuri, K., Tsakalidis, A., Tsichlas, K.: Computation of Repetitions and Regularities on Biological Weighted Sequences. Journal of Computational Biology 13(6), 1214–1231 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Crochemore, M.: An Optimal Algorithm for Computing the Repetitions in a Word. Information Processing Letters 12(5), 244–250 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Gusfield, D.: Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. Cambridge University Press (1997)Google Scholar
  7. 7.
    Guo, Q., Zhang, H., Iliopoulos, C.S.: Computing the λ-covers of a String. Information Sciences 177, 3957–3967 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Iliopoulos, C.S., Moore, D.W.G., Park, K.: Covering a String. Algorithmica 16, 288–297 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Iliopoulos, C.S., Mohamed, M., Smyth, W.F.: New Complexity Results for the k-covers Problem. Information Sciences 181, 251–255 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Iliopoulos, C.S., Smith, W.F.: An On-line Algorithm of Computing a Minimum Set of k-covers of a String. In: Proc. of the Ninth Australian Workshop on Combinatorial Algorithms (AWOCA), pp. 97–106 (1998)Google Scholar
  11. 11.
    Li, Y., Smyth, W.F.: Computing the Cover Array in Linear Time. Algorithmica 32(1), 95–106 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Zhang, H., Guo, Q., Iliopoulos, C.S.: Varieties of Regularities in Weighted Sequences. In: Chen, B. (ed.) AAIM 2010. LNCS, vol. 6124, pp. 271–280. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Zhang, H., Guo, Q., Iliopoulos, C.S.: Loose and Strict Repeats in Weighted Sequences. Protein and Peptide Letters 17(9), 1136–1142 (2010)CrossRefGoogle Scholar
  14. 14.
    The Human Genome Project (HGP), http://www.nbgri.nih.gov/HGP/

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hui Zhang
    • 1
  • Qing Guo
    • 2
  • Costas S. Iliopoulos
    • 3
  1. 1.College of Computer Science and TechnologyZhejiang University of TechnologyHangzhouChina
  2. 2.College of Computer ScienceZhejiang UniversityHangzhouChina
  3. 3.Department of Computer ScienceKing’s College London StrandLondonEngland

Personalised recommendations