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Algorithmic graph theory and perfect graphs. Academic Press, New York, 1980 13. : An improved algorithm for matching biological sequences. J. Mol. Biol. 162, 705–708 (1982) 14. : Improving the practical space and time efficiency of the shortest-paths approach to sum-of-pairs multiple sequence alignment. J. Comput. Biol. 2, 459–472 (1995) 15. : Algorithms on strings, trees and sequences: computer science and computational biology. Cambridge University Press, Cambridge, 1997 16. : Amino acid substitution matrices from protein blocks.

Amino acid substitution matrices from protein blocks. Proceedings of the National Academy of Science 89, 10915–10919 (1992) 17. : Using separation algorithms to generate mixed integer model reformulations. Oper. Res. Lett. 10, 119–128 (1991) 18. : Online dynamic programming with applications to the prediction of rna secondary structure. In: Proceedings of the First Symposium on Discrete Algorithms 1990, pp 503–512 19. LEDA (Library of Efficient Data Types and Algorithms), 2004. com 20. : An exact solution for the segment-to-segment multiple sequence alignment problem.

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. Most of these variables are very unlikely to take the value 1 in an optimal solution. In this section, we describe a simple but successful method to reduce the number of variables.

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