## Section: New Results

Keywords : multiple sequence alignment, integer programming, cutting planes.

### Multiple sequence alignment (ATIPE)

Participants : Ernst Althaus, Stefan Canzar.

In [14] , we propose a cutting plane approach for the alignment of multiple sequences, which is a central problem in computational biology, considering the general case in which (arbitrary) gap costs, besides the customary alignment costs, are specified. An interesting and unusual aspect of our approach is that the three (exponentially large) classes of natural valid inequalities that we considered since the beginning of our study turn out to be both facet defining for the convex hull of the integer solutions and separable in polynomial time. Both the facet defining proofs and the separation algorithms are far from trivial. Experimental results on instances from the BAliBase library of reference alignments show that our method outperforms the best tools developed so far, in that it produces alignments which are better from a biological point of view.

At the moment, we are working in improving the computational efficiency of your approach. The bottleneck of our implementation is the solution of the (exponentially large) linear relaxation of our integer program. We try to develop methods to approximate the value of the linear program efficiently.