Algorithms for Finding a Minimum Repetition Representation of a String

  • Atsuyoshi Nakamura
  • Tomoya Saito
  • Ichigaku Takigawa
  • Hiroshi Mamitsuka
  • Mineichi Kudo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6393)

Abstract

A string with many repetitions can be written compactly by replacing h-fold contiguous repetitions of substring r with (r)h. We refer to such a compact representation as a repetition representation string or RRS, by which a set of disjoint or nested tandem arrays can be compacted. In this paper, we study the problem of finding a minimum RRS or MRRS, where the size of an RRS is defined to be the sum of its component letter sizes and the sizes needed to describe the repetitions (·)h which are defined as wR(h) using a repetition weight function wR. We develop two dynamic programming algorithms to solve the problem. One is CMR that works for any repetition weight function, and the other is CMR-C that is faster but can be applied only when the repetition weight function is constant. CMR-C is an O(w(n + z))-time algorithm using O(n + z) space for a given string with length n, where w and z are the number of distinct primitive tandem repeats and the number of their occurrences, respectively. Since w = O(n) and z = O(nlogn) in the worst case, CMR-C is an O(n2logn)-time O(nlogn)-space algorithm, which is faster than CMR by ((logn)/n)-factor.

Keywords

tandem repeat string algorithm 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Fraenkel, A., Simpson, J.: The exact number of squares in Fibonacci words. Theoretical Computer Science 218, 95–106 (1999)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Gusfield, D., Stoye, J.: Linear time algorithms for finding and representing all the tandem repeats in a string. Journal of Computer and System Sciences 69, 525–546 (2004)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Main, M., Lorentz, R.: An O(nlogn) algorithm for finding all repetitions in a string. Journal of Algorithms 5, 422–432 (1984)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Stoye, J., Gusfield, D.: Simple and Flexible Detection of Contiguous Repeats Using a Suffix Tree. Theoretical Computer Science 270, 843–856 (2002)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Atsuyoshi Nakamura
    • 1
  • Tomoya Saito
    • 1
  • Ichigaku Takigawa
    • 2
  • Hiroshi Mamitsuka
    • 2
  • Mineichi Kudo
    • 1
  1. 1.Hokkaido UniversitySapporoJapan
  2. 2.Institute for Chemical ResearchKyoto UniversityUji, KyotoJapan

Personalised recommendations