### Abstract

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).

Original language | English |
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Title of host publication | Theory and Applications of Models of Computation. TAMC 2010 |

Editors | J. Kratochvil, A. Li, J. Fiala, P. Kolman |

Publisher | Springer |

Pages | 247-257 |

ISBN (Electronic) | 978-3-642-13562-0 |

ISBN (Print) | 978-3-642-13561-3 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

### Publication series

Series | Lecture Notes in Computer Science |
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Volume | 6108 |

## Cite this

Guillemot, S., & Mnich, M. (2010). Kernel and Fast Algorithm for Dense Triplet Inconsistency. In J. Kratochvil, A. Li, J. Fiala, & P. Kolman (Eds.),

*Theory and Applications of Models of Computation. TAMC 2010*(pp. 247-257). Springer. Lecture Notes in Computer Science, Vol.. 6108 https://doi.org/10.1007/978-3-642-13562-0_23