On the Linear-Cost Subtree-Transfer Distance between Phylogenetic Trees

Abstract.

Different phylogenetic trees for the same group of species are often produced either by procedures that use diverse optimality criteria [16] or from different genes [12] in the study of molecular evolution. Comparing these trees to find their similarities and dissimilarities (i.e., distance ) is thus an important issue in computational molecular biology. Several distance metrics including the nearest neighbor interchange (nni) distance and the subtree-transfer distance have been proposed and extensively studied in the literature. This article considers a natural extension of the subtree-transfer distance, called the linear-cost subtree-transfer distance, and studies the complexity and efficient approximation algorithms for this distance as well as its relationship to the nni distance. The linear-cost subtree-transfer model seems more suitable than the (unit-cost) subtree-transfer model in some applications. The following is a list of our results:

1. The linear-cost subtree-transfer distance is in fact identical to the nni distance on unweighted phylogenies.

2. There is an algorithm to compute an optimal linear-cost subtree-transfer sequence between unweighted phylogenies in O(n ⋅ 2 ^O(d) ) time, where d denotes the linear-cost subtree-transfer distance. Such an algorithm is useful when d is small.

3. Computing the linear-cost subtree-transfer distance between two weighted phylogenetic trees is NP-hard, provided we allow multiple leaves of a tree to share the same label (i.e., the trees are not necessarily uniquely labeled).

4. There is an efficient approximation algorithm for computing the linear-cost subtree-transfer distance between weighted phylogenies with performance ratio 2 .