Drawing Tree-Based Phylogenetic Networks with Minimum Number of Crossings

by   Jonathan Klawitter, et al.

In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network N consists of a phylogenetic tree T (a rooted, binary, leaf-labeled tree) and so-called reticulation edges that span between edges of T. The network N is typically visualized by drawing T downward and planar and reticulation edges with one of several different styles. One aesthetic criteria is to minimize the number of crossings between tree edges and reticulation edges. This optimization problem has not yet been researched. We show that, if reticulation edges are drawn x-monotone, the problem is NP-complete, but fixed-parameter tractable in the number of reticulation edges. If, on the other hand, reticulation edges are drawn like "ears", the crossing minimization problem can be solved in quadratic time.



There are no comments yet.


page 1

page 2

page 3

page 4


Drawing Two Posets

We investigate the problem of drawing two posets of the same ground set ...

Covering Tree-Based Phylogenetic Networks

Tree-based phylogenetic networks, which may be roughly defined as leaf-l...

An Ongoing Project to Improve the Rectilinear and the Pseudolinear Crossing Constants

A drawing of a graph in the plane is pseudolinear if the edges of the d...

Crossing Minimization in Perturbed Drawings

Due to data compression or low resolution, nearby vertices and edges of ...

Extending Simple Drawings

Simple drawings of graphs are those in which each pair of edges share at...

On the edge-length ratio of 2-trees

We study planar straight-line drawings of graphs that minimize the ratio...

Recovering tree-child networks from shortest inter-taxa distance information

Phylogenetic networks are a type of leaf-labelled, acyclic, directed gra...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.