Kaikoura tree theorems: computing the maximum agreement subtree
Information Processing Letters
Tree compatibility and inferring evolutionary history
Journal of Algorithms
On the agreement of many trees
Information Processing Letters
Regular Article: Extension Operations on Sets of Leaf-Labeled Trees
Advances in Applied Mathematics
On the complexity of comparing evolutionary trees
Discrete Applied Mathematics - Special volume on computational molecular biology
Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms
SIAM Journal on Computing
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the domatic number
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Faster exact algorithms for hard problems: a parameterized point of view
Discrete Mathematics
Regular Article: A Structured Family of Clustering and Tree Construction Methods
Advances in Applied Mathematics
Introduction to Algorithms
An O(nlog n) Algorithm for the Maximum Agreement Subtree Problem for Binary Trees
SIAM Journal on Computing
Approximating the Complement of the Maximum Compatible Subset of Leaves of k Trees
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
On the approximation of computing evolutionary trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Maximum agreement and compatible supertrees
Journal of Discrete Algorithms
Discovering Frequent Agreement Subtrees from Phylogenetic Data
IEEE Transactions on Knowledge and Data Engineering
Linear time 3-approximation for the MAST problem
ACM Transactions on Algorithms (TALG)
From Gene Trees to Species Trees through a Supertree Approach
LATA '09 Proceedings of the 3rd International Conference on Language and Automata Theory and Applications
Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Building species trees from larger parts of phylogenomic databases
Information and Computation
On the approximation of computing evolutionary trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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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 data sets, 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. The improves on a known result for MAST and proves fixed-parameter tractability for MCT.