Extending the Hardness of RNA Secondary Structure Comparison

  • Guillaume Blin
  • Guillaume Fertin
  • Irena Rusu
  • Christine Sinoquet
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4614)

Abstract

In molecular biology, RNA structure comparison is of great interest to help solving problems as different as phylogeny reconstruction, prediction of molecule folding and identification of a function common to a set of molecules. Lin et al. [6] proposed to define a similarity criterion between RNA structures using a concept of edit distance ; they named the corresponding problem Edit. Recently, Blin et al. [3] showed that another problem, the Longest Arc-Preserving Common Subsequence problem (or Lapcs), is in fact a subproblem of Edit. This relationship between those two problems induces the hardness of what was the last open case for the Edit problem, Edit (Nested, Nested), which corresponds to computing the edit distance between two secondary structures without pseudoknots. Nevertheless, Lapcs is a very restricted subproblem of Edit: in particular, it corresponds to a given system of editing costs, whose biological relevance can be discussed ; hence, giving a more precise categorization of the computational complexity of the Edit problem remains of interest. In this paper, we answer this question by showing that Edit(Nested, Nested) is NP-complete for a large class of instances, not overlapping with the ones used in the proof for Lapcs, and which represent more biologically relevant cost systems.

Keywords

computational biology RNA structures arc-annotated sequences edit distance NP-hardness 

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References

  1. 1.
    Bernhart, F., Kainen, P.C.: The book thickness of a graph. Journal of Combinatorial Theory, Series B 27(3), 320–331 (1979)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Biedl, T., Kant, G., Kaufmann, M.: On triangulating planar graphs under the four-connectivity constraint. Algorithmica 19, 427–446 (1997)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blin, G., Touzet, H.: How to compare arc-annotated sequences: the alignment hierarchy. In: Crestani, F., Ferragina, P., Sanderson, M. (eds.) SPIRE 2006. LNCS, vol. 4209, pp. 291–303. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Evans, P.A.: Algorithms and Complexity for Annotated Sequence Analysis. PhD thesis, University of Victoria (1999)Google Scholar
  5. 5.
    Lin, G.H., Chen, Z.Z., Jiang, T., Wen, J.: The longest common subsequence problem for sequences with nested arc annotations. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 444–455. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  6. 6.
    Lin, G.H., Ma, B., Zhang, K.: Edit distance between two RNA structures. In: RECOMB 2001. Proceedings of the 5th International Conference on Computational Biology, pp. 211–220. ACM Press, New York (2001)CrossRefGoogle Scholar
  7. 7.
    Sankoff, D., Kruskal, B.: Time Warps, String Edits and Macromolecules: the Theory and Practice of Sequence Comparison. Addison-Wesley, Reading (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Guillaume Blin
    • 1
  • Guillaume Fertin
    • 2
  • Irena Rusu
    • 2
  • Christine Sinoquet
    • 2
  1. 1.IGM-LabInfo - UMR CNRS 8049 - Université de Marne-la-ValléeFrance
  2. 2.LINA - FRE CNRS 2729 - Université de NantesFrance

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