相关论文: On the neighbourhoods of trees

A central theme in phylogenetics is the reconstruction and analysis of evolutionary trees from a given set of data. To determine the optimal search methods for reconstructing trees, it is crucial to understand the size and structure of the…

Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree…

Network rearrangement operations like SNPR (SubNet Prune and Regraft), a recent generalisation of rSPR (rooted Subtree Prune and Regraft), induce a metric on phylogenetic networks. To search the space of these networks one important…

We describe a kernel of size 9k-8 for the NP-hard problem of computing the Tree Bisection and Reconnect (TBR) distance k between two unrooted binary phylogenetic trees. We achieve this by extending the existing portfolio of reduction rules…

The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm…

A rearrangement operation makes a small graph-theoretical change to a phylogenetic network to transform it into another one. For unrooted phylogenetic trees and networks, popular rearrangement operations are tree bisection and reconnection…

The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…

The Neighbor-Joining algorithm is a recursive procedure for reconstructing trees that is based on a transformation of pairwise distances between leaves. We present a generalization of the neighbor-joining transformation, which uses…

The reconstruction of phylogenies from DNA or protein sequences is a major task of computational evolutionary biology. Common phenomena, notably variations in mutation rates across genomes and incongruences between gene lineage histories,…

Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…

We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…

We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…

Three standard subtree transfer operations for binary trees, used in particular for phylogenetic trees, are: tree bisection and reconnection ($TBR$), subtree prune and regraft ($SPR$) and rooted subtree prune and regraft ($rSPR$). For a…

Many popular algorithms for searching the space of leaf-labelled trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are…

In 2007, Eickmeyer et al. showed that the tree topologies outputted by the Neighbor-Joining (NJ) algorithm and the balanced minimum evolution (BME) method for phylogenetic reconstruction are each determined by a polyhedral subdivision of…

The tree-metric theorem provides a necessary and sufficient condition for a dissimilarity matrix to be a tree metric, and has served as the foundation for numerous distance-based reconstruction methods in phylogenetics. Our main result is…

Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary…

A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…

The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…

Tree rearrangements such as Nearest Neighbor Interchange (NNI) and Subtree Prune and Regraft (SPR) are commonly used to explore phylogenetic treespace. Computing distances based on them, however, is often intractable, so the efficiently…