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Schlagwörter:
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Zusammenfassung:
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.
