Related papers: Comparing and Aggregating Partially Resolved Trees
A chief problem in phylogenetics and database theory is the computation of a maximum consistent tree from a set of rooted or unrooted trees. A standard input are triplets, rooted binary trees on three leaves, or quartets, unrooted binary…
Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…
We study the inference of network archaeology in growing random geometric graphs. We consider the root finding problem for a random nearest neighbor tree in dimension $d \in \mathbb{N}$, generated by sequentially embedding vertices…
The search for similarity and dissimilarity measures on phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in phylogenetic databases, and the assessment of clustering results in…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…
Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…
There are several tools available to infer phylogenetic trees, which depict the evolutionary relationships among biological entities such as viral and bacterial strains in infectious outbreaks, or cancerous cells in tumor progression trees.…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Edit distance between trees is a natural generalization of the classical edit distance between strings, in which the allowed elementary operations are contraction, uncontraction and relabeling of an edge. Demaine et al. [ACM Trans. on…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…
It is known that PQ-symmetric maps on the boundary characterize the quasi-isometry type of visual hyperbolic spaces, in particular, of geodesically complete \br-trees. We define a map on pairs of PQ-symmetric ultrametric spaces which…
In this paper, we study metric trees, without any finiteness restrictions. For subsets of such trees, a condition that guarantees that the Hausdorff and Gromov--Hausdorff distances from the subset to the entire metric tree are the same is…
We introduce a scale-free method for testing the proportionality of branch lengths between two phylogenetic trees that have the same topology and contain the same set of taxa. This method scales both trees to a total length of 1 and sums up…
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…
Distances on merge trees facilitate visual comparison of collections of scalar fields. Two desirable properties for these distances to exhibit are 1) the ability to discern between scalar fields which other, less complex topological…
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…
The subtree prune-and-regraft (SPR) distance metric is a fundamental way of comparing evolutionary trees. It has wide-ranging applications, such as to study lateral genetic transfer, viral recombination, and Markov chain Monte Carlo…
The path-difference metric is one of the oldest distances for the comparison of fully resolved phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the mean value of the square of the…
Gromov-Hausdorff (GH) distance is a natural way to measure the distortion between two metric spaces. However, there has been only limited algorithmic development to compute or approximate this distance. We focus on computing the…