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
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
Fast comparison of evolutionary trees
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Maximum agreement and compatible supertrees
Journal of Discrete Algorithms
Linear time 3-approximation for the MAST problem
ACM Transactions on Algorithms (TALG)
On the approximability of the Maximum Agreement SubTree and Maximum Compatible Tree problems
Discrete Applied Mathematics
On the approximation of computing evolutionary trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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We address a combinatorial problem which arises in computational phylogenetics. In this problem we are given a set of unrooted (not necessarily binary) trees each leaf-labelled by the same set S, and we wish to remove a minimum number of leaves so that the resultant trees share a common refinement (i.e. they are "compatible". If we assume the input trees are all binary, then this is simply the Maximum Agreement Subtree problem (MAST), for which much is already known. However, if the input trees need not be binary, then the problem is much more computationally intensive: it is NP-hard for just two trees, and solvable in polynomial time for any number k of trees when all trees have bounded degree. In this paper we present an O(k2n2 4-approximation algorithm and an O(k2n3 3-approximation algorithm for the general case of this problem.