Determining the evolutionary tree using experiments
Journal of Algorithms
Fast Updating of Well-Balanced Trees
SWAT '90 Proceedings of the 2nd Scandinavian Workshop on Algorithm Theory
Improving Partial Rebuilding by Using Simple Balance Criteria
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Efficient Merging, Construction, and Maintenance of Evolutionary Trees
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
The randomized complexity of maintaining the minimum
Nordic Journal of Computing
Balanced randomized tree splitting with applications to evolutionary tree constructions
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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 tight upper and lower bounds for the problem of constructing evolutionary trees in the experiment model. We describe an algorithm which constructs an evolutionary tree of n species in time O(nd logd n) using at most n⌈d/2⌉(log2ċd/2ċ 1 n+O(1)) experiments for d 2, and at most n(log n+O(1)) experiments for d = 2, where d is the degree of the tree. This improves the previous best upper bound by a factor Θ(log d). For d = 2 the previously best algorithm with running time O(n log n) had a bound of 4n log n on the number of experiments. By an explicit adversary argument, we show an Ω(nd logd n) lower bound, matching our upper bounds and improving the previous best lower bound by a factor Θ(logd n). Central to our algorithm is the construction and maintenance of separator trees of small height, which may be of independent interest.