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Given a set X of taxa, a phylogenetic X-tree T that is only partially resolved, and a collection of characters on X, we consider the problem of finding a resolution (refinement) of T that minimizes the parsimony score of the given characters. Previous work has shown that this problem has a polynomial time solution provided certain strong constraints are imposed on the input. In this paper we provide a new algorithm for this problem, and show that it is fixed parameter tractable under more general conditions.

Refining Phylogenetic Trees Given Additional Data: An Algorithm Based on Parsimony