Parameterized Complexity of the Arc-Preserving Subsequence Problem

  • Dániel Marx
  • Ildikó Schlotter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6410)


We study the Arc-Preserving Subsequence (APS) problem with unlimited annotations. Given two arc-annotated sequences P and T, this problem asks if it is possible to delete characters from T to obtain P. Since even the unary version of APS is NP-hard, we used the framework of parameterized complexity, focusing on a parameterization of this problem where the parameter is the number of deletions we can make. We present a linear-time FPT algorithm for a generalization of APS, applying techniques originally designed to give an FPT algorithm for Induced Subgraph Isomorphism on interval graphs [12].


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alber, J., Gramm, J., Guo, J., Niedermeier, R.: Computing the similarity of two sequences with nested arc annotations. Theor. Comput. Sci. 312(2-3), 337–358 (2004)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Blin, G., Fertin, G., Rizzi, R., Vialette, S.: What makes the Arc-Preserving Subsequence problem hard? In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2005. LNCS, vol. 3515, pp. 860–868. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Damaschke, P.: A remark on the subsequence problem for arc-annotated sequences with pairwise nested arcs. Inf. Process. Lett. 100(2), 64–68 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Monographs in Computer Science. Springer, New York (1999)CrossRefMATHGoogle Scholar
  5. 5.
    Evans, P.A.: Algorithms and complexity for annotated sequence analysis. PhD thesis, University of Victoria, Canada (1999)Google Scholar
  6. 6.
    Evans, P.A.: Finding common subsequences with arcs and pseudoknots. In: Crochemore, M., Paterson, M. (eds.) CPM 1999. LNCS, vol. 1645, pp. 270–280. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. In: Texts in Theoretical Computer Science. An EATCS Series, p. 493. Springer, Heidelberg (2006)Google Scholar
  8. 8.
    Gramm, J., Guo, J., Niedermeier, R.: Pattern matching for arc-annotated sequences. ACM Trans. Algorithms 2(1), 44–65 (2006)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Jiang, T., Lin, G., Ma, B., Zhang, K.: The longest common subsequence problem for arc-annotated sequences. J. Discrete Algorithms 2(2), 257–270 (2004)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Lin, G., Chen, Z.-Z., Jiang, T., Wen, J.: The longest common subsequence problem for sequences with nested arc annotations. J. Comput. Syst. Sci. 65(3), 465–480 (2002)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Ma, B., Wang, L., Zhang, K.: Computing similarity between RNA structures. Theor. Comput. Sci. 276(1-2), 111–132 (2002)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Marx, D., Schlotter, I.: Cleaning interval graphs. CoRR abs/1003.1260 (2010) arXiv:1003.1260 [cs.DS]Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dániel Marx
    • 1
  • Ildikó Schlotter
    • 2
  1. 1.Tel Aviv UniversityIsrael
  2. 2.Budapest University of Technology and EconomicsHungary

Personalised recommendations