Kernel and Fast Algorithm for Dense Triplet Inconsistency

We study the parameterized complexity of inferring supertrees from sets of rooted triplets, an important problem in phylogenetics. For a set l of labels and a dense set \mathcal r\mathcal r of triplets distinctly leaf-labeled by 3-subsets of l we seek a tree distinctly leaf-labeled by l and containing all but at most p triplets from \mathcal r\mathcal r as homeomorphic subtree. Our results are the first polynomial kernel for this problem, with o(p 2) labels, and a subexponential fixed-parameter algorithm running in time 2^{o(p^{1/3} \log p)} + o(n^4)2^{o(p^{1/3} \log p)} + o(n^4).