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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.
combination network, phylogenetic network, parsimony method, NP-hardness, approximability, dynamic programming
Louxin Zhang, Nguyen Bao Nguyen, Wing-Kin Sung, C. Thach Nguyen, "Reconstructing Recombination Network from Sequence Data: The Small Parsimony Problem", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 4, no. , pp. 394-402, July-September 2007, doi:10.1109/tcbb.2007.1018
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