Fixed-Parameter Algorithms for Finding Agreement Supertrees
We study the agreement supertree approach for combining rooted phylogenetic trees when the input trees do not fully agree on the relative positions of the taxa. Two approaches to dealing with such conflicting input trees are considered. The first is to contract a set of edges in the input trees so that the resulting trees have an agreement supertree. We show that this problem is NP-complete and give an FPT algorithm for the problem parameterized by the number of input trees and the number of edges contracted. The second approach is to remove a set of taxa from the input trees so that the resulting trees have an agreement supertree. An FPT algorithm for this problem when the input trees are all binary was given by Guillemot and Berry (2010). We give an FPT algorithm for the more general case when the input trees have arbitrary degree.
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