A Simple Fixed Parameter Tractable Algorithm for Computing the Hybridization Number of Two (Not Necessarily Binary) Trees

摘要

Here, we present a new fixed parameter tractable algorithm to compute the hybridization number $(r)$ of two rooted, not necessarily binary phylogenetic trees on taxon set $({{cal X}})$ in time $((6^r r!) cdot poly(n))$, where $(n=vert {{cal X}}vert)$. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on $({{cal X}})$, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem.