### Abstract

Multiple sequence alignment is an important problem in computational biology. We study the Maximum Trace formulation introduced by Kececioglu [Kec91]. 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 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 [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.

Original language | English (US) |
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Pages | 241-250 |

Number of pages | 10 |

State | Published - Jan 1 1997 |

Externally published | Yes |

Event | Proceedings of the 1997 1st Annual International Conference on Computational Molecular Biology, RECOMB - Santa Fe, NM, USA Duration: Jan 20 1997 → Jan 23 1997 |

### Other

Other | Proceedings of the 1997 1st Annual International Conference on Computational Molecular Biology, RECOMB |
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City | Santa Fe, NM, USA |

Period | 1/20/97 → 1/23/97 |

### ASJC Scopus subject areas

- Engineering(all)

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## Cite this

*Branch-and-cut algorithm for multiple sequence alignment*. 241-250. Paper presented at Proceedings of the 1997 1st Annual International Conference on Computational Molecular Biology, RECOMB, Santa Fe, NM, USA, .