A Propagator for Maximum Weight String Alignment with Arbitrary Pairwise Dependencies

  • Alessandro Dal Palù
  • Mathias Möhl
  • Sebastian Will
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6308)


The optimization of weighted string alignments is a well studied problem recurring in a number of application domains and can be solved efficiently. The problem becomes MAX-SNP-hard as soon as arbitrary pairwise dependencies among the alignment edges are introduced. We present a global propagator for this problem which is based on efficiently solving a relaxation of it. In the context of bioinformatics, the problem is known as alignment of arc-annotated sequences, which is e.g. used for comparing RNA molecules. For a restricted version of this alignment problem, we show that a constraint program based on our propagator is on par with state of the art methods. For the general problem with unrestricted dependencies, our tool constitutes the first available method with promising applications in this field.


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  1. 1.
    Bauer, M., Klau, G.W., Reinert, K.: Accurate multiple sequence-structure alignment of RNA sequences using combinatorial optimization. BMC Bioinformatics 8, 271 (2007)CrossRefGoogle Scholar
  2. 2.
    Blin, G., Fertin, G., Rusu, I., Sinoquet, C.: Extending the hardness of RNA secondary structure comparison. In: Chen, B., Paterson, M., Zhang, G. (eds.) ESCAPE 2007. LNCS, vol. 4614, pp. 140–151. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Caprara, A., Lancia, G.: Structural alignment of large-size proteins via lagrangian relaxation. In: Proceedings of the Sixth Annual International Conference on Computational Biology (RECOMB 2002), pp. 100–108. ACM Press, New York (2002)CrossRefGoogle Scholar
  4. 4.
    Gotoh, O.: An improved algorithm for matching biological sequences. Journal of Molecular Biology 162, 705–708 (1982)CrossRefGoogle Scholar
  5. 5.
    Hoeve, W.-J., Pesant, G., Rousseau, L.-M.: On global warming: Flow-based soft global constraints. Journal of Heuristics 12(4-5), 347–373 (2006)MATHCrossRefGoogle Scholar
  6. 6.
    Jiang, T., Lin, G., Ma, B., Zhang, K.: A general edit distance between RNA structures. Journal of Computational Biology 9(2), 371–388 (2002)CrossRefGoogle Scholar
  7. 7.
    Marinescu, R., Dechter, R.: And/or branch-and-bound search for combinatorial optimization in graphical models. Artif. Intell. 173(16-17), 1457–1491 (2009)MATHCrossRefGoogle Scholar
  8. 8.
    McCaskill, J.S.: The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29(6-7), 1105–1119 (1990)CrossRefGoogle Scholar
  9. 9.
    Möhl, M., Will, S., Backofen, R.: Lifting prediction to alignment of RNA pseudoknots. Journal of Computational Biology (2010) (accepted)Google Scholar
  10. 10.
    Smith, T.F., Waterman, M.S.: Comparison of biosequences. Adv. Appl. Math. 2, 482–489 (1981)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Trick, M.A.: A dynamic programming approach for consistency and propagation for knapsack constraints. Annals OR 118(1-4), 73–84 (2003)MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Will, S., Reiche, K., Hofacker, I.L., Stadler, P.F., Backofen, R.: Inferring non-coding RNA families and classes by means of genome-scale structure-based clustering. PLOS Computational Biology 3(4), e65 (2007)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alessandro Dal Palù
    • 1
  • Mathias Möhl
    • 2
  • Sebastian Will
    • 2
    • 3
  1. 1.Dipartimento di MatematicaUniversità degli Studi di ParmaParmaItaly
  2. 2.Bioinformatics, Institute of Computer ScienceAlbert-Ludwigs-UniversitätFreiburgGermany
  3. 3.Computation and Biology LabCSAIL, MITCambridgeUSA

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