The complexity of comparing multiply-labelled trees by extending phylogenetic-tree metrics

03/15/2018
by   Manuel Lafond, et al.
0

A multilabeled tree (or MUL-tree) is a rooted tree in which every leaf is labelled by an element from some set, but in which more than one leaf may be labelled by the same element of that set. In phylogenetics, such trees are used in biogeographical studies, to study the evolution of gene families, and also within approaches to construct phylogenetic networks. A multilabelled tree in which no leaf-labels are repeated is called a phylogenetic tree, and one in which every label is the same is also known as a tree-shape. In this paper, we consider the complexity of computing metrics on MUL-trees that are obtained by extending metrics on phylogenetic trees. In particular, by restricting our attention to tree shapes, we show that computing the metric extension on MUL-trees is NP complete for two well-known metrics on phylogenetic trees, namely, the path-difference and Robinson Foulds distances. We also show that the extension of the Robinson Foulds distance is fixed parameter tractable with respect to the distance parameter. The path distance complexity result allows us to also answer an open problem concerning the complexity of solving the quadratic assignment problem for two matrices that are a Robinson similarity and a Robinson dissimilarity, which we show to be NP-complete. We conclude by considering the maximum agreement subtree (MAST) distance on phylogenetic trees to MUL-trees. Although its extension to MUL-trees can be computed in polynomial time, we show that computing its natural generalization to more than two MUL-trees is NP-complete, although fixed-parameter tractable in the maximum degree when the number of given trees is bounded.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/02/2019

A rearrangement distance for fully-labelled trees

The problem of comparing trees representing the evolutionary histories o...
research
05/11/2021

Tree Edit Distance with Variables. Measuring the Similarity between Mathematical Formulas

In this article, we propose tree edit distance with variables, which is ...
research
09/11/2019

Tree congruence: quantifying similarity between dendrogram topologies

Tree congruence metrics are typically global indices that describe the s...
research
07/24/2020

Computing nearest neighbour interchange distances between ranked phylogenetic trees

Many popular algorithms for searching the space of leaf-labelled trees a...
research
11/01/2022

A Near-Linear Kernel for Two-Parsimony Distance

The maximum parsimony distance d_MP(T_1,T_2) and the bounded-state maxim...
research
12/08/2017

Deciding the existence of a cherry-picking sequence is hard on two trees

Here we show that deciding whether two rooted binary phylogenetic trees ...
research
02/13/2020

On Two Measures of Distance between Fully-Labelled Trees

The last decade brought a significant increase in the amount of data and...

Please sign up or login with your details

Forgot password? Click here to reset