Reconstructing Recombination Network from Sequence Data: The Small Parsimony Problem

The small parsimony problem is studied for reconstructing recombination networks from sequence data. The small parsimony problem is polynomial-time solvable for phylogenetic trees. However, the problem is proven NP-hard even for galled recombination networks. A dynamic programming algorithm is also developed to solve the small parsimony problem. It takes
O
(
dn
2
<sup>3

h</sup>
) time on an input recombination network over length-
d
sequences in which there are
h
recombination and
n
-
h
tree nodes.