Related papers: On the complexity of computing MP distance between…
Supertree methods are tree reconstruction techniques that combine several smaller gene trees (possibly on different sets of species) to build a larger species tree. The question of interest is whether the reconstructed supertree converges…
The Persistent-Phylogeny Model is an extension of the widely studied Perfect-Phylogeny Model, encompassing a broader range of evolutionary phenomena. Biological and algorithmic questions concerning persistent phylogeny have been intensely…
In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [BNS02] denoted as the MRSO problem. The problem is known to be…
Lineage tracing, the tracking of living cells as they move and divide, is a central problem in biological image analysis. Solutions, called lineage forests, are key to understanding how the structure of multicellular organisms emerges. We…
There exist several methods dealing with the reconstruction of rooted phylogenetic networks explaining different evolutionary histories given by rooted binary phylogenetic trees. In practice, however, due to insufficient information of the…
We consider the problem of estimating species trees from unrooted gene tree topologies in the presence of incomplete lineage sorting, a common phenomenon that creates gene tree heterogeneity in multilocus datasets. One popular class of…
The matching distance is a pseudometric on multi-parameter persistence modules, defined in terms of the weighted bottleneck distance on the restriction of the modules to affine lines. It is known that this distance is stable in a reasonable…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
Given two binary trees on $N$ labeled leaves, the quartet distance between the trees is the number of disagreeing quartets. By permuting the leaves at random, the expected quartets distance between the two trees is…
Flips in triangulations of convex polygons arise in many different settings. They are isomorphic to rotations in binary trees, define edges in the 1-skeleton of the Associahedron and cover relations in the Tamari Lattice. The complexity of…
Given two rooted phylogenetic trees on the same set of taxa X, the Maximum Agreement Forest problem (MAF) asks to find a forest that is, in a certain sense, common to both trees and has a minimum number of components. The Maximum Acyclic…
An accurate assessment of a model's complexity is crucial for topics such as interpretation, generalization, and model selection. However, most existing complexity measures either rely on heuristic assumptions or are computationally…
Computing supertrees is a central problem in phylogenetics. The supertree method that is by far the most widely used today was introduced in 1992 and is called Matrix Representation with Parsimony analysis (MRP). Matrix Representation using…
When we apply comparative phylogenetic analyses to genome data, it is a well-known problem and challenge that some of given species (or taxa) often have missing genes. In such a case, we have to impute a missing part of a gene tree from a…
We consider distance labeling schemes for trees: given a tree with $n$ nodes, label the nodes with binary strings such that, given the labels of any two nodes, one can determine, by looking only at the labels, the distance in the tree…
Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…
The asymmetric tropical distance is a distance measure on the tropical torus $\mathbb{R}^n/\mathbb{R}\mathbf{1}$ and in particular on the Bergman fan $B(K_N) \subseteq \mathbb{R}^{\binom{N}{2}}/\mathbb{R}\mathbf{1}$ of the complete…
Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…
Mixed-integer linear programming (MILP) is a powerful tool for addressing a wide range of real-world problems, but it lacks a clear structure for comparing instances. A reliable similarity metric could establish meaningful relationships…
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived…