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SIAM Journal on Computing
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STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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Advances in Applied Mathematics
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SIAM Journal on Computing
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STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
An O(nlog n) Algorithm for the Maximum Agreement Subtree Problem for Binary Trees
SIAM Journal on Computing
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
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
Rooted Maximum Agreement Supertrees
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COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
An O(nlog n)-time algorithm for the maximum constrained agreement subtree problem for binary trees
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
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Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Hierarchical clustering using constraints
ISBRA'08 Proceedings of the 4th international conference on Bioinformatics research and applications
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IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Kernel and fast algorithm for dense triplet inconsistency
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Fixed-Parameter algorithms for finding agreement supertrees
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
Fixed-parameter tractability of the maximum agreement supertree problem
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
Kernel and fast algorithm for dense triplet inconsistency
Theoretical Computer Science
Gene tree correction for reconciliation and species tree inference: Complexity and algorithms
Journal of Discrete Algorithms
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Given a set of leaf-labelled trees with identical leaf sets, the MAST problem, respectively MCT problem, consists of finding a largest subset of leaves such that all input trees restricted to these leaves are isomorphic, respectively compatible. In this paper, we propose extensions of these problems to the context of supertree inference, where input trees have non-identical leaf sets. This situation is of particular interest in phylogenetics. The resulting problems are called SMAST and SMCT. A sufficient condition is given that identifies cases where these problems can be solved by resorting to MAST and MCT as subproblems. This condition is met, for instance, when only two input trees are considered. Then we give algorithms for SMAST and SMCT that benefit from the link with the subtree problems. These algorithms run in time linear to the time needed to solve MAST, respectively MCT, on an instance of the same or smaller size. It is shown that arbitrary instances of SMAST and SMCT can be turned in polynomial time into instances composed of trees with a bounded number of leaves. SMAST is shown to be W[2]-hard when the considered parameter is the number of input leaves that have to be removed to obtain the agreement of the input trees. A similar result holds for SMCT. Moreover, the corresponding optimization problems, that is the complements of SMAST and SMCT, cannot be approximated in polynomial time within any constant factor, unless P=NP. These results also hold when the input trees have a bounded number of leaves. The presented results apply to both collections of rooted and unrooted trees.