Related papers: L-infinity optimization to linear spaces and phylo…
In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…
In this paper, we introduce a specific type of Euclidean tree called LED (Leaves of Equal Depth) tree. LED trees can be used in computational phylogeny, since they are a natural representative of the time evolution of a set of species in a…
The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is ``optimal'' when the algorithm…
In this paper, we present a factor 16 approximation algorithm for the following NP-hard distance fitting problem: given a finite set X and a distance d on X, find a Robinsonian distance dR on X minimizing the l\infty-error ||d - dR||\infty…
Phylogenetic networks are a generalization of phylogenetic trees that allow for representation of reticulate evolution. Recently, a space of unrooted phylogenetic networks was introduced, where such a network is a connected graph in which…
We propose a new space of phylogenetic trees which we call wald space. The motivation is to develop a space suitable for statistical analysis of phylogenies, but with a geometry based on more biologically principled assumptions than…
A classic problem in unsupervised learning and data analysis is to find simpler and easy-to-visualize representations of the data that preserve its essential properties. A widely-used method to preserve the underlying hierarchical structure…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree. Yet most reconstruction methods like ML do not explicitly maximize this accuracy. To address this problem, we propose a…
Ultrametric matrices have a rich structure that is not apparent from their definition. Notably, the subclass of strictly ultrametric matrices are covariance matrices of certain weighted rooted binary trees. In applications, these matrices…
Merge trees are a type of graph-based topological summary that tracks the evolution of connected components in the sublevel sets of scalar functions. They enjoy widespread applications in data analysis and scientific visualization. In this…
The matching distance is a computationally tractable topological measure to compare multi-filtered simplicial complexes. We design efficient algorithms for approximating the matching distance of two bi-filtered complexes to any desired…
Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov…
In this article we study the treewidth of the \emph{display graph}, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display…
We present the first sub-quadratic time algorithm that with high probability correctly reconstructs phylogenetic trees for short sequences generated by a Markov model of evolution. Due to rapid expansion in sequence databases, such very…
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…
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 Subtree…
The maximum parsimony phylogenetic tree reconstruction problem is NP-hard, presenting a computational bottleneck for classical computing and motivating the exploration of emerging paradigms like quantum computing. To this end, we design…
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic…
We propose an extension of tree-based space-partitioning indexing structures for data with low intrinsic dimensionality embedded in a high dimensional space. We call this extension an Angle Tree. Our extension can be applied to both…