Normalized Similarity of RNA Sequences

  • Rolf Backofen
  • Danny Hermelin
  • Gad M. Landau
  • Oren Weimann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3772)


We introduce a normalized version of the LCS metric as a new local similarity measure for comparing two RNAs. An \(\mathcal{O}(n^{2}m{\rm lg}m)\) time algorithm is presented for computing the maximum normalized score of two RNA sequences, where n and m are the lengths of the sequences and nm. This algorithm has the same time complexity as the currently best known global LCS algorithm.


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  1. 1.
    Alber, J., Gramm, J., Guo, J., Niedermeier, R.: Towards optimally solving the longest common subsequence problem for sequences with nested arc annotations in linear time. In: Apostolico, A., Takeda, M. (eds.) CPM 2002. LNCS, vol. 2373, pp. 99–114. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Apostolico, A., Guerra, C.: The longest common subsequence problem revisited. Algorithmica 2, 315–336 (1987)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Arslan, A.N., Eǧecioğlu, Ö., Pevzner, P.A.: A new approach to sequence alignment: normalized sequence alignment. Bioinformatics 17(4), 327–337 (2001)CrossRefGoogle Scholar
  4. 4.
    Bille, P.: A survey on tree edit distance and related problems. Theoretical Computer Science 337, 217–239 (2005)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Chartrand, P., Meng, X.-H., Singer, R.H., Long, R.M.: Structural elements required for the localization of ASH1 mRNA and of a green fluorescent protein reporter particle in vivo. Current Biology 9, 333–336 (1999)CrossRefGoogle Scholar
  6. 6.
    Couzin, J.: Breakthrough of the year. Small RNAs make big splash. Science 298(5602), 2296–2297 (2002)CrossRefGoogle Scholar
  7. 7.
    Efraty, N., Landau, G.M.: Sparse normalized local alignment. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 333–346. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Evans, P.A.: Algorithms and complexity for annotated sequence analysis. PhD thesis, University of Alberta (1999)Google Scholar
  9. 9.
    Gramm, J., Guo, J., Niedermeier, R.: Pattern matching for arc annotated sequences. In: Agrawal, M., Seth, A.K. (eds.) FSTTCS 2002. LNCS, vol. 2556, pp. 182–193. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  10. 10.
    Hirschberg, D.S.: Algorithms for the longest common subsequence problem. Journal of the ACM 24(4), 664–675 (1977)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Hunt, J.W., Szymanski, T.G.: A fast algorithm for computing longest common subsequences. Communications of the ACM 20(5), 350–353 (1977)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Jiang, T., Lin, G.-H., Ma, B., Zhang, K.: The longest common subsequence problem for arc-annotated sequences. In: Giancarlo, R., Sankoff, D. (eds.) CPM 2000. LNCS, vol. 1848, pp. 154–165. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Klein, P.N.: Computing the Edit-Distance between Unrooted Ordered Trees. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 91–102. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  14. 14.
    Moore, P.B.: Structural motifs in RNA. Annual review of biochemistry 68, 287–300 (1999)CrossRefGoogle Scholar
  15. 15.
    Shasha, D., Zhang, K.: Simple fast algorithms for the editing distance between trees and related problems. SIAM Journal on Computing 18(6), 1245–1262 (1989)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Smith, T.F., Waterman, M.S.: The identification of common molecular subsequences. Journal of Molecular Biology 147, 195–197 (1981)CrossRefGoogle Scholar
  17. 17.
    Zhang, K.: Computing similarity between RNA secondary structures. In: Proc. of the IEEE joint symposium on Intelligence and Systems conference, pp. 126–132 (1998)Google Scholar
  18. 18.
    Zuker, M.: On finding all suboptimal foldings of an RNA molecule. Science 244(4900), 48–52 (1989)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Research 9(1), 133–148 (1981)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Rolf Backofen
    • 1
  • Danny Hermelin
    • 2
  • Gad M. Landau
    • 3
    • 4
  • Oren Weimann
    • 2
  1. 1.Institute of Computer ScienceFriedrich-Schiller Universität Jena, Jena Center for BioinformaticsGermany
  2. 2.Department of Computer ScienceUniversity of HaifaIsrael
  3. 3.Department of Computer ScienceUniversity of HaifaHaifaIsrael
  4. 4.Department of Computer and Information SciencePolytechnic UniversityNew YorkUSA

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