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 proved NP-hard even for galled recombination networks. A dynamic programming algorithm is also developed to solve the small parsimony problem. It takes O(dn2(3h)) time on an input recombination network over length-d sequences in which there are h recombination and n - h tree nodes.