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#### A branch-and-cut algorithm for multiple sequence alignment

##### MPS-Authors
/persons/resource/persons45277

Reinert,  Knut
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons44909

Lenhof,  Hans-Peter
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45092

Mutzel,  Petra
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45021

Mehlhorn,  Kurt
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons44750

Kececioglou,  John
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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##### Fulltext (public)

1996-1-028
(Any fulltext), 11KB

##### Supplementary Material (public)
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##### Citation

Reinert, K., Lenhof, H.-P., Mutzel, P., Mehlhorn, K., & Kececioglou, J.(1996). A branch-and-cut algorithm for multiple sequence alignment (MPI-I-1996-1-028). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-A037-B
##### Abstract
Multiple sequence alignment is an important problem in computational biology. We study the Maximum Trace formulation introduced by Kececioglu~\cite{Kececioglu91}. We first phrase the problem in terms of forbidden subgraphs, which enables us to express Maximum Trace as an integer linear-programming problem, and then solve the integer linear program using methods from polyhedral combinatorics. The trace {\it polytope\/} is the convex hull of all feasible solutions to the Maximum Trace problem; for the case of two sequences, we give a complete characterization of this polytope. This yields a polynomial-time algorithm for a general version of pairwise sequence alignment that, perhaps suprisingly, does not use dynamic programming; this yields, for instance, a non-dynamic-programming algorithm for sequence comparison under the 0-1 metric, which gives another answer to a long-open question in the area of string algorithms \cite{PW93}. For the multiple-sequence case, we derive several classes of facet-defining inequalities and show that for all but one class, the corresponding separation problem can be solved in polynomial time. This leads to a branch-and-cut algorithm for multiple sequence alignment, and we report on our first computational experience. It appears that a polyhedral approach to multiple sequence alignment can solve instances that are beyond present dynamic-programming approaches.