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

By Althaus E.

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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 }.

5; 1 18 29:42. 0; 10 50 7:49. 6; 1 14 9:24. 1; 1 27 40:38. 0; 1 14 2:08. 0]; 1 51 10:02:04. 4; 1 16 6:55. 7]; 1 45 12:33:06. 3]; 1 34 10:08:14. 1]; 1 120 10:23:22. 4]; 9 149 10:06:15. 8]; 1 109 10:28:33. 0]; 1 92 10:30:51. 0]; 1 30 10:37:44. 3]; 1 31 10:00:06. 3. Comparison with other programs We compared our algorithm with the most recent structural alignments algorithms, considering the overall best performing programs from the survey [27]: PRRP, ClustalX, and Dialign, together with a recently published program T-Coffee [22], which generally outperforms the other programs.

S j |; i, j = 1, . . , k; i < j, z{v i ,v j l m−1 } ≥ z{v i ,v j } + x{v i ,v j l m l m−1 } , l = 1, . . , |s i |; m = 2, . . , |s j |; i, j = 1, . . , k; i < j. This corresponds to introducing O(n2 ) new variables and constraints. Variable reduction Even for rather small instances, the number of variables in our ILP k i j 2 formulation is very large, namely there are k−1 j =i+1 |s ||s | = O(n ) edge varii=1 ables and ki=1 (k − 1) |s 2|+1 = O(n3 ) arc variables. For example, an instance with 5 strings of length 100 has 201, 000 variables.

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