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Journal of Combinatorial Optimization

, Volume 16, Issue 2, pp 127–154 | Cite as

A Lagrangian relaxation approach for the multiple sequence alignment problem

  • Ernst Althaus
  • Stefan CanzarEmail author
Open Access
Article

Abstract

We present a branch-and-bound (bb) algorithm for the multiple sequence alignment problem (MSA), one of the most important problems in computational biology. The upper bound at each bb node is based on a Lagrangian relaxation of an integer linear programming formulation for MSA. Dualizing certain inequalities, the Lagrangian subproblem becomes a pairwise alignment problem, which can be solved efficiently by a dynamic programming approach. Due to a reformulation w.r.t. additionally introduced variables prior to relaxation we improve the convergence rate dramatically while at the same time being able to solve the Lagrangian problem efficiently. Our experiments show that our implementation, although preliminary, outperforms all exact algorithms for the multiple sequence alignment problem. Furthermore, the quality of the alignments is among the best computed so far.

Keywords

Sequence comparison Lagrangian relaxation Branch and bound 

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Copyright information

© The Author(s) 2008

Open AccessThis is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Max-Planck Institut für InformatikSaarbrückenGermany

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