Related papers: Constructing minimal phylogenetic networks from so…
Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. Given a set of clusters, a network is said to represent these clusters in the "softwired" sense if, for each cluster in the input set, at least one…
In [2] it was proven that the Cass algorithm is a polynomial-time algorithm for constructing level<=2 networks from clusters. Here we demonstrate, for each k>=0, a polynomial-time algorithm for constructing level-k phylogenetic networks…
Given a dense triplet set $\mathcal{T}$, there arise two interesting questions: Does there exists any phylogenetic network consistent with $\mathcal{T}$? And if so, can we find an effective algorithm to construct one? For cases of networks…
For a given set $\mathcal{L}$ of species and a set $\mathcal{T}$ of triplets on $\mathcal{L}$, one wants to construct a phylogenetic network which is consistent with $\mathcal{T}$, i.e which represents all triplets of $\mathcal{T}$. The…
It has remained an open question for some time whether, given a set of not necessarily binary (i.e. "nonbinary") trees T on a set of taxa X, it is possible to determine in time f(r).poly(m) whether there exists a phylogenetic network that…
Phylogenetic networks generalize phylogenetic trees by representing reticulate evolution. Tree-based networks and their support trees have been extensively studied, but not all networks are tree-based. To measure how far such networks are…
We define a general variant of the graph clustering problem where the criterion of density for the clusters is (high) connectivity. In {\sc Clustering to Given Connectivities}, we are given an $n$-vertex graph $G$, an integer $k$, and a…
Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network…
A phylogenetic network is a directed acyclic graph that visualises an evolutionary history containing so-called reticulations such as recombinations, hybridisations or lateral gene transfers. Here we consider the construction of a simplest…
We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is…
Network reconstruction lies at the heart of phylogenetic research. Two well studied classes of phylogenetic networks include tree-child networks and level-$k$ networks. In a tree-child network, every non-leaf node has a child that is a tree…
Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet…
A phylogenetic network is a graph-theoretical tool that is used by biologists to represent the evolutionary history of a collection of species. One potential way of constructing such networks is via a distance-based approach, where one is…
Phylogenetic networks are directed acyclic graphs that depict the genomic evolution of related taxa. Reticulation nodes in such networks (nodes with more than one parent) represent reticulate evolutionary events, such as recombination,…
We give a Hasse-diagram characterization of when a clustering system $\mathcal C$ on a finite taxa set $X$ is the hardwired clustering system $C_N$ of a rooted level-$k$ network. For each non-trivial block $B$ of $H=\mathcal H[\mathcal C]$,…
We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…
Genetic and comparative genomic studies indicate that extant genomes are more properly considered to be a fusion product of random mutations over generations and genomic material transfers between individuals of different lineages. This has…
We consider connectivity-augmentation problems in a setting where each potential new edge has a nonnegative cost associated with it, and the task is to achieve a certain connectivity target with at most p new edges of minimum total cost.…
Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer.…
Tree-child networks, one of the prominent network classes in phylogenetics, have been introduced for the purpose of modeling reticulate evolution. Recently, the first author together with Gittenberger and Mansouri (2019) showed that the…