### 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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Title of host publication | Proceedings of thr Annual International Conference on Computational Molecular Biology, RECOMB |

Publisher | ACM |

Pages | 241-250 |

Number of pages | 10 |

State | Published - 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 |
---|---|

City | Santa Fe, NM, USA |

Period | 1/20/97 → 1/23/97 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*Proceedings of thr Annual International Conference on Computational Molecular Biology, RECOMB*(pp. 241-250). ACM.

**Branch-and-cut algorithm for multiple sequence alignment.** / Reinert, K.; Lenhof, H. P.; Mutzel, P.; Mehlhorn, K.; Kececioglu, John D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of thr Annual International Conference on Computational Molecular Biology, RECOMB.*ACM, pp. 241-250, Proceedings of the 1997 1st Annual International Conference on Computational Molecular Biology, RECOMB, Santa Fe, NM, USA, 1/20/97.

}

TY - GEN

T1 - Branch-and-cut algorithm for multiple sequence alignment

AU - Reinert, K.

AU - Lenhof, H. P.

AU - Mutzel, P.

AU - Mehlhorn, K.

AU - Kececioglu, John D

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0030697670&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030697670&partnerID=8YFLogxK

M3 - Conference contribution

SP - 241

EP - 250

BT - Proceedings of thr Annual International Conference on Computational Molecular Biology, RECOMB

PB - ACM

ER -