Balanced randomized tree splitting with applications to evolutionary tree constructions

Abstract

We present a new technique called balanced randomized tree splitting. It is useful in constructing unknown trees recursively. By applying it we obtain two new results on eficient construction of evolutionary trees: a new upper time-bound on the problem of constructing an evolutionary tree from experiments, and a relatively fast approximation algorithm for the maximum agreement subtree problem for binary trees for which the maximum number of leaves in an optimal solution is large. We also present new lower bounds for the problem of constructing an evolutionary tree from experiments and for the problem of constructing a tree from an ultrametric distance matrix.