# MPI-I-96-1-028

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

### Reinert, Knut and Lenhof, Hans-Peter and Mutzel, Petra and Mehlhorn, Kurt and Kececioglou, John D.

**MPI-I-96-1-028**. November** **1996, 15 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

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.

Acknowledgement:** **

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1996-1-028

**BibTeX**
`@TECHREPORT{``ReinertLenhofMutzelMehlhornKececioglou96``,`

` AUTHOR = {Reinert, Knut and Lenhof, Hans-Peter and Mutzel, Petra and Mehlhorn, Kurt and Kececioglou, John D.},`

` TITLE = {A branch-and-cut algorithm for multiple sequence alignment},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-96-1-028},`

` MONTH = {November},`

` YEAR = {1996},`

` ISSN = {0946-011X},`

`}`