A fast algorithm for constructing trees from distance matrices
Information Processing Letters
Determining the evolutionary tree using experiments
Journal of Algorithms
Maximum Agreement Subtree in a Set of Evolutionary Trees: Metrics and Efficient Algorithms
SIAM Journal on Computing
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Fast algorithms for constructing optimal trees from quartets
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Fast comparison of evolutionary trees
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Balanced randomized tree splitting with applications to evolutionary tree constructions
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The Complexity of Constructing Evolutionary Trees Using Experiments
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Computing the Quartet Distance between Evolutionary Trees in Time O(n log2 n)
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
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We present new techniques of efficiently merging and updating partial evolutionary trees in the so called experiment model. We show that two partial evolutionary trees for disjoint sets of species can be merged using experiments in time O(dn), where n is the size of the resulting evolutionary tree and d is its maximum degree. We prove our upper time bound for merging evolutionary trees to be asymptotically optimal. We show also that after O(n log n)-time preprocessing, a partial evolutionary tree can be maintained under a sequence of m species insertions or deletions in time O(dm log(n + m)). By applying our algorithm for merging evolutionary trees, or alternatively, our algorithm for updating evolutionary trees, we obtain an O(dn log n)-time bound on the problem of constructing an evolutionary tree of size n and maximum degree d from experiments. The classic O(n log n)-time bound on sorting in the comparison model can be seen as a very special case of this upper bound.