Faster algorithms for optimal multiple sequence alignment based on pairwise comparisons

Yonatan Bilu, Pankaj K. Agarwal, Rachel Kolodny

Research output: Contribution to journalArticlepeer-review


Multiple Sequence Alignment (MSA) is one of the most fundamental problems in computational molecular biology. The running time of the best known scheme for finding an optimal alignment, based on dynamic programming, increases exponentially with the number of input sequences. Hence, many heuristics were suggested for the problem. We consider a version of the MSA problem where the goal is to find an optimal alignment in which matches are restricted to positions in predefined matching segments. We present several techniques for making the dynamic programming algorithm more efficient, while still finding an optimal solution under these restrictions. We prove that it suffices to find an optimal alignment of the predefined sequence segments, rather than single letters, thereby reducing the input size and thus improving the running time. We also identify "shortcuts" that expedite the dynamic programming scheme. Empirical study shows that, taken together, these observations lead to an improved running time over the basic dynamic programming algorithm by 4 to 12 orders of magnitude, while still obtaining an optimal solution. Under the additional assumption that matches between segments are transitive, we further improve the running time for finding the optimal solution by restricting the search space of the dynamic programming algorithm.

Original languageEnglish
Pages (from-to)408-422
Number of pages15
JournalIEEE/ACM Transactions on Computational Biology and Bioinformatics
Issue number4
StatePublished - Oct 2006
Externally publishedYes

Bibliographical note

Funding Information:
The authors would like to thank Chris Lee and Nati Linial for enlightening discussions, Eylon Portugaly for his help in implementing the algorithm, and the referees for many helpful comments. Y. Bilu is supported by the Dewey David Stone Postdoctoral Fellowship and UniNet EC NEST consortium contract number 12990. P.K. Agarwal is supported by US National Science Foundation (NSF) grants CCR-00-86013, EIA-98-70724, EIA-01-31905, and CCR-02-04118, and by a grant from the US-Israel Binational Science Foundation. R. Kolodny is supported by NSF grant CCR-00-86013. Part of this work was done while Y. Bilu was at the School of Engineering and Computer Science, The Hebrew University of Jerusalem, and R. Kolodny was at the Department of Computer Science, Stanford University and visiting Duke University.


  • Algorithms
  • Dynamic programming
  • Multiple sequence alignment
  • Shortest path

ASJC Scopus subject areas

  • Applied Mathematics
  • Genetics
  • Biotechnology


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  • Faster algorithms for optimal Multiple Sequence Alignment based on pairwise comparisons

    Agarwal, P. K., Bilu, Y. & Kolodny, R., 2005, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). p. 315-327 13 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 3692 LNBI).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Open Access

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