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.
November 1996, 15 pages.
.
Status: available - back from printing
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.
-
- Attachement: MPI-I-96-1-028.ps (202 KBytes)
URL to this document: https://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},
}