By Althaus E.

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**Extra resources for A branch-and-cut algorithm for multiple sequence alignment**

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S j | + 1, each having l weight w(v j ,v j m p−1 )i m l p j j and representing the realization of gap arc (vm , vp−1 )i in the align- ment. It is easy to check that the optimal alignment between strings s i and s j corresponds to the longest (arc-weighed) path from n{v i ,v j } to n{v i ,v j in Qij with the property } 1 1 |s i |+1 |s j |+1 that no consecutive arcs in the path are red. Such a path can be found in linear time in the size of Qij , which is O(|s i ||s j | max{|s i |, |s j |}), by using two labels for each node, one for the longest path and the other for the longest path whose last arc is green.

Bioinformatics 15 (3), 203–210 (1999) 21. : The practical use of the A∗ algorithm for exact multiple sequence alignment. J. Comput. Biol. 7(5), 655–673 (2000) 22. : T-coffee : A novel method for fast and accurate multiple sequence alignment. J. Mol. Biol. 302, 205–217 (2000) 23. : A Polyhedral Approach to Sequence Alignment Problems. PhD thesis, Universit¨at des Saarlandes, 1999 24. : A branch-and-cut algorithm for multiple sequence alignment. In: Proceedings of the First Annual International Conference on Computational Molecular Biology (RECOMB-97), 1997, pp 241–249 25.

A Polyhedral Approach to Sequence Alignment Problems. PhD thesis, Universit¨at des Saarlandes, 1999 24. : A branch-and-cut algorithm for multiple sequence alignment. In: Proceedings of the First Annual International Conference on Computational Molecular Biology (RECOMB-97), 1997, pp 241–249 25. K. Reinert, J. Stoye, and T. Will. An iterative methods for faster sum-of-pairs multiple sequence alignment. BIOINFORMATICS 16(9):808–814, 2000. 26. SCIL–Symbolic Constraints for Integer Linear programming, 2002.

### A branch-and-cut algorithm for multiple sequence alignment by Althaus E.

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