The multiple sequence alignment problem in biology
SIAM Journal on Applied Mathematics
Sequence comparison with mixed convex and concave costs
Journal of Algorithms
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
A branch-and-cut algorithm for multiple sequence alignment
RECOMB '97 Proceedings of the first annual international conference on Computational molecular biology
On-line dynamic programming with applications to the prediction of RNA secondary structure
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Heuristic Method for the Set Covering Problem
Operations Research
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We present a branch-and-bound (bb) algorithm for the multiple sequence alignment problem (MSA), one of the most important problems in computational biology. The upper bound at each bb node is based on a Lagrangian relaxation of an integer linear programming formulation for MSA. Dualizing certain inequalities, the Lagrangian subproblem becomes a pairwise alignment problem, which can be solved efficiently by a dynamic programming approach. Due to a reformulation w.r.t. additionally introduced variables prior to relaxation we improve the convergence rate dramatically while at the same time being able to solve the Lagrangian problem efficiently. Our experiments show that our implementation, although preliminary, outperforms all exact algorithms for the multiple sequence alignment problem.