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Constructing Minimal Phylogenetic Networks from Softwired Clusters is Fixed Parameter Tractable

Abstract : Here we show that, given a set of clusters C on a set of taxa X , where |X | = n, it is possible to determine in time f(k) · poly(n) whether there exists a level-≤ k network (i.e. a network where each biconnected component has reticulation number at most k) that represents all the clusters in C in the softwired sense, and if so to construct such a network. This extends a result from [20] which showed that the problem is polynomial-time solvable for fixed k. By defining "k-reticulation generators" analogous to "level-k generators", we then extend this fixed parameter tractability result to the problem where k refers not to the level but to the reticulation number of the whole network.
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Steven Kelk, Celine Scornavacca. Constructing Minimal Phylogenetic Networks from Softwired Clusters is Fixed Parameter Tractable. Algorithmica, Springer Verlag, 2014, 68 (4), pp.886-915. ⟨10.1007/s00453-012-9708-5⟩. ⟨hal-02154980⟩

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