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By Althaus E.

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In addition, we provide an average for each group. The results show that our approach was on average superior to all other programs. Our comparison with other programs reveals that computing near-optimal alignments does pay off in terms of quality, because our approach produced on average the biologically most meaningful alignments. On the other hand, it has to be remarked that, for the larger instances in the library, the LPs that arise are at present not solvable within acceptable time by our approach, unless we use a very small value of δ in the heuristic preprocessing, which has the effect A branch-and-cut algorithm for multiple sequence alignment 423 Table 4.

282 (51) of eliminating a wide set of useful variables. Currently, our method is not competitive for these instances. 5. Conclusions and further work A comparison of the known multiple sequence alignment tools shows that almost all of these programs are heuristics that try to find good approximations of the optimal multiple alignment. Each of these tools makes use of its own scoring function. We have presented for the first time an approach to general multiple sequence alignment with arbitrary gap costs.

Sli of s i with substring s1 . . sm of s j , for l = 1, . . , |s i | and m = 1, . . , |s j |. Moreover, in a completely analogous way and in the same running time one can find the value ωij (l, m) of the optimal alignment of substring sli . . s|si i | of s i with substring j j sm . . s|s j | of s j . The sum of the values of all the pairwise optimal alignments is clearly an upper bound on the value of the optimal alignment, called the pairwise upper bound. For convenience, let σ ij denote the sum of the values of the optimal alignments between all string pairs different from {s i , s j }.

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