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How to Compare Arc-Annotated Sequences: The Alignment Hierarchy

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Book cover String Processing and Information Retrieval (SPIRE 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4209))

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Abstract

We describe a new unifying framework to express comparison of arc-annotated sequences, which we call alignment of arc-annotated sequences. We first prove that this framework encompasses main existing models, which allows us to deduce complexity results for several cases from the literature. We also show that this framework gives rise to new relevant problems that have not been studied yet. We provide a thorough analysis of these novel cases by proposing two polynomial time algorithms and an NP-completeness proof. This leads to an almost exhaustive study of alignment of arc-annotated sequences.

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References

  1. Bernhart, F., Kainen, B.: The book thickness of a graph. J. Comb. Theory Series B 27, 320–331 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  2. Biedl, T.C., Kant, G., Kaufmann, M.: On triangulating planar graphs under the four-connectivity constraint. Algorithmica 19(4), 427–446 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  3. Blin, G., Fertin, G., Rusu, I., Sinoquet, C.: RNA sequences and the EDIT(NESTED, NESTED) problem. technical report - LINA (2003)

    Google Scholar 

  4. Crochemore, M., Hermelin, D., Landau, G.M., Vialette, S.: Approximating the 2-interval pattern problem. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 426–437. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Dulucq, S., Touzet, H.: Decomposition algorithms for the tree edit distance problem. Journal of Discrete Algorithms 3(2-4), 448–471 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Evans, P.: Algorithms and Complexity for Annotated Sequences Analysis. PhD thesis, University of Victoria (1999)

    Google Scholar 

  7. Herrbach, C., Denise, A., Dulucq, S., Touzet, H.: A polynomial algorithm for comparing RNA secondary structures using a full set of operations

    Google Scholar 

  8. Jiang, T., Lin, G., Ma, B., Zhang, K.: A general edit distance between RNA structures. Journal of Computational Biology 9(2), 371–388 (2002)

    Article  Google Scholar 

  9. Jiang, T., Lin, G., Ma, B., Zhang, K.: The longest common subsequence problem for arc-annotated sequences. Journal of Discrete Algorithms, 257–270 (2004)

    Google Scholar 

  10. Jiang, T., Wang, L., Zhang, K.: Alignment of trees - an alternative to tree edit. Theoretical Computer Science 143(1), 137–148 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  11. Klein, P.: Computing the edit-distance between unrooted ordered trees. In: 6th European Symposium on Algorithms, pp. 91–102 (1998)

    Google Scholar 

  12. Lin, G., Chen, Z.-Z., jiang, T., Wen, J.: The longest common subsequence problem for sequences with nested arc annotations. Journal of Computer and System Sciences 65, 465–480 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lin, G., Ma, B., Zhang, K.: Edit distance between two rna structures. In: RECOMB, pp. 211–220 (2001)

    Google Scholar 

  14. Ma, B., Wang, L., Zhang, K.: Computing similarity between RNA structures. Theoretical Computer Sciences 276, 111–132 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  15. Tai, K.C.: The tree-to-tree correction problem. Journal of the Association for Comput. Machi. 26, 422–433 (1979)

    MATH  MathSciNet  Google Scholar 

  16. Vialette, S.: On the computational complexity of 2-interval pattern matching. Theoretical Computer Science 312(2-3), 223–249 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  17. Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems. SIAM Journal of Computing 18(6), 1245–1262 (1989)

    Article  MATH  MathSciNet  Google Scholar 

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Blin, G., Touzet, H. (2006). How to Compare Arc-Annotated Sequences: The Alignment Hierarchy. In: Crestani, F., Ferragina, P., Sanderson, M. (eds) String Processing and Information Retrieval. SPIRE 2006. Lecture Notes in Computer Science, vol 4209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11880561_24

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  • DOI: https://doi.org/10.1007/11880561_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45774-9

  • Online ISBN: 978-3-540-45775-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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