Efficient Chaining of Seeds in Ordered Trees

  • Julien Allali
  • Cédric Chauve
  • Pascal Ferraro
  • Anne-Laure Gaillard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)


We consider here the problem of chaining seeds in ordered trees. Seeds are mappings between two trees Q and T and a chain is a subset of non overlapping seeds that is consistent with respect to postfix order and ancestrality. This problem is a natural extension of a similar problem for sequences, and has applications in computational biology, such as mining a database of RNA secondary structures. For the chaining problem with a set of m constant size seeds, we describe an algorithm with complexity O(m 2 log(m)) in time and O(m 2) in space.


Time Complexity Maximum Chain Order Tree Valid Mapping Border Node 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Allali, J., Chauve, C., Ferraro, P., Gaillard, A.-L.: Efficient chaining of seeds in ordered trees. arXiv:1007.0942v1 [q-bio.QM] (2010)Google Scholar
  2. 2.
    Altschul, S.F., Gish, W., Miller, W., Myers, E.W., Lipman, D.J.: Basic local alignment search tool. J. Mol. Biol. 215(3), 403–410 (1990)CrossRefGoogle Scholar
  3. 3.
    Aluru, S. (ed.): Handbook of Computational Molecular Biology. CRC Press, Boca Raton (2005)zbMATHGoogle Scholar
  4. 4.
    Backofen, R., Will, S.: Local sequence-structure motifs in RNA. J. Bioinform. Comput. Biol. 2(4), 681–698 (2004)CrossRefGoogle Scholar
  5. 5.
    Demaine, E.D., Mozes, S., Rossman, B., Weimann, O.: An optimal decomposition algorithm for tree edit distance. ACM Trans. Algorithms 6(1), Article 2 (2009)Google Scholar
  6. 6.
    Gardner, P.P., Daub, J., Tate, J.G., et al.: Rfam: updates to the RNA families database. Nucleic Acids Res. 37(Database issue), D136–D140 (2009)CrossRefGoogle Scholar
  7. 7.
    Gusfield, D.: Algorithms on Strings, Trees and Sequences. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  8. 8.
    Heyne, S., Will, S., Beckstette, M., Backofen, R.: Lightweight comparison of RNAs based on exact sequence-structure matches. Bioinformatics 25(16), 2095–2102 (2009)CrossRefGoogle Scholar
  9. 9.
    Jiang, T., Lin, G., Ma, B., Zhang, K.: A general edit distance between RNA structures. J. Comput. Biol. 9(2), 371–388 (2002)CrossRefGoogle Scholar
  10. 10.
    Joseph, D., Meidanis, J., Tiwari, P.: Determining DNA sequence similarity using maximum independent set algorithms for interval graphs. In: Nurmi, O., Ukkonen, E. (eds.) SWAT 1992. LNCS, vol. 621, pp. 326–337. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  11. 11.
    Lipman, D.J., Pearson, W.R.: Rapid and sensitive protein similarity searches. Science 227(4693), 1435–1441 (1985)CrossRefGoogle Scholar
  12. 12.
    Lozano, A., Pinter, R.Y., Rokhlenko, O., Valiente, G., Ziv-Ukelson, M.: Seeded tree alignment. IEEE/ACM TCBB 5(4), 503–513 (2008)Google Scholar
  13. 13.
    Ohlebusch, E., Abouelhoda, M.I.: Chaining Algorithms and Applications in Comparative Genomics. In: Handbook of Computational Molecular Biology. CRC Press, Boca Raton (2005)Google Scholar
  14. 14.
    Pearson, W.R., Lipman, D.J.: Improved tools for biological sequence comparison. PNAS 85(8), 2444–2448 (1988)CrossRefGoogle Scholar
  15. 15.
    Pedersen, J.S., et al.: Identification and classification of conserved RNA secondary structures in the human genome. PLoS Comput. Biol. 2(4), e33 (2006)CrossRefGoogle Scholar
  16. 16.
    Shapiro, B.A., Zhang, K.: Comparing multiple RNA secondary structures using tree comparisons. CABIOS 6, 309–318 (1990)Google Scholar
  17. 17.
    Zhang, K., Shasha, D.: Simple fast algorithms for the editing distance between trees and related problems. SIAM J. Comput. 18(6), 1245–1262 (1989)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Julien Allali
    • 1
    • 2
    • 3
  • Cédric Chauve
    • 3
  • Pascal Ferraro
    • 1
    • 2
    • 4
  • Anne-Laure Gaillard
    • 1
  1. 1.LaBRIUniversité Bordeaux 1, IPB, CNRSFrance
  2. 2.Pacific Institute for Mathematical Sciences and CNRS UMI3069France
  3. 3.Department of MathematicsSimon Fraser UniversityCanada
  4. 4.Department of Computer ScienceUniversity of CalgaryCanada

Personalised recommendations