Alignment between Two Multiple Alignments

  • Bin Ma
  • Zhuozhi Wang
  • Kaizhong Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2676)


Alignment of two multiple alignments arises naturally when constructing approximate multiple sequence alignments progressively. In this paper, we consider the problem of alignment of two multiple alignments with SP-score and linear gap costs.

When there is no gap opening cost, this problem can be solved using the well-known dynamic programming algorithm for two sequences by viewing each column in the multiple alignments as an element. However if there are gap opening costs (sometimes referred as affine gap costs) then the problem becomes non-trivial. Gotoh [4] suggested a procedure for this problem and stated that “the total arithmetic operations used is close to (quadratic) in typical cases”. Kececioglu and Zhang [7] gave heuristic algorithms based on optimistic and pessimistic gap counts and conjectured that this problem is NP-complete. In this paper we prove that this problem is indeed NP-complete and therefore settle this open problem. We then propose another heuristic algorithm for this problem.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E.L. Anson and G. Myers. Realigner: a program for refining dna sequence multialignments. In Proceedings of the First ACM conference on Computational Molecular Biology, pages 9–13, 1997.Google Scholar
  2. 2.
    P. Bonizzoni and G. Della Vedova. The complexity of multiple sequence alignment with sp-score that is a metric. Theorectical Computer Science, 259(1):63–79, 2001.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    O. Gotoh. An improved algorithm for matching biological sequences. Journal of Molecular Biology, 162:705–708, 1982.CrossRefGoogle Scholar
  4. 4.
    O. Gotoh. Optimal alignment between groups of sequences and its application to multiple sequence alignment. Computer Application in the Biosciences, 9(3):361–370, 1993.Google Scholar
  5. 5.
    D. Gusfield. Efficient methods for multiple sequence alignment with guaranteed error bounds. Bulletin of Mathematical Biology, 55:141–154, 1993.zbMATHGoogle Scholar
  6. 6.
    W. Just. Computational complexity of multiple sequence alignment with sp-score. Journal of computational biology, 8(6):615–623, 2001.CrossRefMathSciNetGoogle Scholar
  7. 7.
    J. D. Kececioglu and W. Zhang. Aligning alignments. In Proceedings of the Ninth Symposium on Combinatorial Pattern Matching, Lecture Notes in Computer Science 1448, pages 189–208. Springer-Verlag, 1998.CrossRefGoogle Scholar
  8. 8.
    G. Myers, S. Selznick, Z. Zhang, and W. Miller. Progressive multiple alignment with constraints. In Proceedings of the First ACM conference on Computational Molecular Biology, pages 220–225, 1997.Google Scholar
  9. 9.
    S.B. Needleman and C.D. Wunsch. A general method applicable to the search for similarities in the amino acid sequence of two proteins. Journal of Molecular Biology, 48:443–453, 1970.CrossRefGoogle Scholar
  10. 10.
    C.H. Papadimitriou and M. Yannakakis. Optimization, approximation, and complexity classes. J. Comput. System Sciences, 43:425–440, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    L. Wang and T. Jiang. On the complexity of multiple sequence alignment. Journal of computational biology, 1(4):337–448, 1994.CrossRefGoogle Scholar
  12. 12.
    Z. Wang and K. Zhang. Alignment between rna structures. In Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 2136, pages 690–702. Springer-Verlag, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Bin Ma
    • 1
  • Zhuozhi Wang
    • 1
  • Kaizhong Zhang
    • 1
  1. 1.Dept. of Computer ScienceUniversity of Western OntarioLondonCanada

Personalised recommendations