APPROXIMATING THE MAXIMUM ISOMORPHIC AGREEMENT SUBTREE IS HARD

Abstract

The Maximum Isomorphic Agreement Subtree [Formula: see text] problem is one of the simplest versions of the Maximum Interval Weight Agreement Subtree method [Formula: see text] which is used to compare phylogenies. More precisely [Formula: see text] allows to provide a subset of the species such that the exact distances between species in such subset are preserved among all evolutionary trees considered. In this paper, the approximation complexity of the MIT problem is investigated, showing that it cannot be approximated in polynomial time within factor log δn for any δ > 0 unless NP ⊆ DTIME(2polylog n) for instances containing three trees. Moreover, we show that such result can be strengthened whenever instances of the [Formula: see text] problem can contain an arbitrary number of trees, since [Formula: see text] shares the same approximation lower bound of [Formula: see text].