## DIMACS TR: 2007-21

## Algorithms and Heuristics for Constrained Generalized Tree Alignment Problem

### Author: Dr. Srikrishnan Divakaran

**
ABSTRACT
**

In generalized tree alignment problem, we are given a set S of
k biologically related sequences and we are interested in
a minimum cost evolutionary tree for S. In many instances of
this problem partial topology of the phylogenetic tree for S
is known. In such instances, we would like to make use of this
knowledge to restrict the tree topologies that we consider
and construct a biologically relevant minimum cost evolutionary
tree. So, in this paper we propose the following natural
generalization of the generalized tree alignment problem, a
problem known to be MAX-SNP Hard, stated as follows:
*Constrained Generalized Tree Alignment Problem*:
Given a set
S of
k related sequences and a phylogenetic forest comprising
of node-disjoint phylogenetic trees that specify the topological
constraints that an evolutionary tree of
S needs to satisfy,
construct a minimum cost evolutionary tree for
S.

In this paper, we present constant approximation algorithms for
the constrained generalized tree alignment problem. For the
generalized tree alignment problem, a special case of this
problem, our algorithms provide a guaranteed error bound of
2-2/k and do not exclude any tree topology a priori.

Paper Available at:
ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2007/2007-21.pdf

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