Locating a Tree in a Phylogenetic Network in Quadratic Time

Computing nearest neighbour interchange distances between ranked phylogenetic trees

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 given by pairs of trees connected by one rearrangement operation (sometimes called a move). Most popular are the classical nearest neighbour interchange, subtree prune and regraft, and tree bisection and reconnection moves. The problem of computing distances, however, is NP-hard in each of these graphs, making tree inference and comparison algorithms challengin…

Gain-loss-duplication models on a phylogeny: exact algorithms for computing the likelihood and its gradient

Gene gain-loss-duplication models are commonly based on continuous-time birth-death processes. Employed in a phylogenetic context, such models have been increasingly popular in studies of gene content evolution across multiple genomes. While the applications are becoming more varied and demanding, bioinformatics methods for probabilistic inference on copy numbers (or integer-valued evolutionary characters, in general) are scarce. We describe a flexible probabilistic framework for phylogenetic gene-loss-duplication models. The framework is based on a novel elementary representation by dependent…

Solving Tree Containment Problem for Reticulation-visible Networks with Optimal Running Time

Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in the class of binary network. Recently, it was proven to be solvable in cubic time, and later in quadratic time for the class of general reticulation visible networks. In this paper, we further improve the time complexity into linear time.

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

Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf vertex is the parent of a tree vertex or a leaf. Up to a certain equivalence, it has been recently shown that, under two different types of weightings, edge-weighted tree-child networks are determined by their collection of distances between each pair of taxa. However, the size of these collections can be exponential in the size of the taxa set. In this paper,…

识别问题的紧（双）指数下界：定位支配集与测试覆盖

Tight (Double) Exponential Bounds for Identification Problems: Locating-Dominating Set and Test Cover

本文针对定位支配集和测试覆盖两个识别问题，证明了以树宽和解大小为参数时的紧双指数下界，并给出匹配下界的算法，其中定位支配集是首个在解大小参数下具有二次指数下界的问题。

A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm is combinatorial and its running time is quadratic in the input size. To prove the approximation guarantee, we construct a feasible dual solution for a novel linear programming formulation. In addition, we show this linear program is stronger than previously known formulations, and we giv…

NOC NOC，谁在那里？树孩子网络和正规网络的聚类系统

NOC NOC, who's there? Clustering systems of tree-child and normal networks

本文通过非重叠覆盖（NOC）性质刻画正规和树孩子网络的聚类系统，证明NOC等价于包含可见性，给出二次上界与多项式时间识别算法，并探讨了其在枚举、序理论和最小集合覆盖等方面的推论。

Gene Tree Construction and Correction using SuperTree and Reconciliation

The supertree problem asking for a tree displaying a set of consistent input trees has been largely considered for the reconstruction of species trees. Here, we rather explore this framework for the sake of reconstructing a gene tree from a set of input gene trees on partial data. In this perspective, the phylogenetic tree for the species containing the genes of interest can be used to choose among the many possible compatible "supergenetrees", the most natural criteria being to minimize a reconciliation cost. We develop a variety of algorithmic solutions for the construction and correction of…

绘制二元Tanglegrams：一个实验评估

Drawing Binary Tanglegrams: An Experimental Evaluation

二叉缠结图是一对<S，T>二叉树，其叶集一一对应;匹配的叶由树间边连接。对于应用，例如在遗传学或软件工程中，需要绘制无交叉的个体树。一个自然的优化问题，表示tanglegram布局问题，因此，以尽量减少交叉之间的树边缘的数量。tanglegram布局问题是一个NP难问题，目前在应用领域和理论上都得到了广泛的研究。在本文中，我们提出了一个实验比较的递归算法的Buchin等人，我们的变种，他们的算法，算法层次排序的霍尔滕和范维克，和一个整数二次规划，产生最佳解决方案。