Improved Parametrized Complexity of Maximum Agreement Subtree and Maximum Compatible Tree problems - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles IEEE/ACM Transactions on Computational Biology and Bioinformatics Year : 2006

Improved Parametrized Complexity of Maximum Agreement Subtree and Maximum Compatible Tree problems

Abstract

Given a set of evolutionary trees on a same set of taxa, the maximum agreement subtree problem (MAST), respectively maximum compatible tree problem (MCT), consists of finding a largest subset of taxa such that all input trees restricted to these taxa are isomorphic, respectively compatible. These problems have several applications in phylogenetics such as the computation of a consensus of phylogenies obtained from different datasets, the identification of species subjected to horizontal gene transfers and, more recently, the inference of supertrees, e.g. Trees Of Life. We provide two linear time algorithms to check the isomorphism, respectively compatibility, of a set of trees or otherwise identify a conflict between the trees with respect to the relative location of a small subset of taxa. Then, we use these algorithms as subroutines to solve MAST and MCT on rooted or unrooted trees of unbounded degree. More precisely, we give exact fixed-parameter tractable algorithms, whose running time is uniformly polynomial when the number of taxa on which the trees disagree is bounded. This improves on a known result for MAST and proves fixed-parameter tractability for MCT.
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Dates and versions

lirmm-00131835 , version 1 (19-02-2007)

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Vincent Berry, François Nicolas. Improved Parametrized Complexity of Maximum Agreement Subtree and Maximum Compatible Tree problems. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2006, 3 (3), pp.289-302. ⟨10.1109/TCBB.2006.39⟩. ⟨lirmm-00131835⟩
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