Related papers: Reconstructing Arbitrary Trees from Traces in the …
In this work we study the interleaving distance between merge trees from a combinatorial point of view. We use a particular type of matching between trees to obtain a novel formulation of the distance. With such formulation, we tackle the…
In this paper, we consider the problem of reconstructing a directed graph using path queries. In this query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries. For a…
Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…
The unordered tree edit distance is a natural metric to compute distances between trees without intrinsic child order, such as representations of chemical molecules. While the unordered tree edit distance is MAX SNP-hard in principle, it is…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
We consider a natural variant of the well-known Feedback Vertex Set problem, namely the problem of deleting a small subset of vertices or edges to a full binary tree. This version of the problem is motivated by real-world scenarios that are…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
In the beautifully simple-to-state problem of trace reconstruction, the goal is to reconstruct an unknown binary string $x$ given random "traces" of $x$ where each trace is generated by deleting each coordinate of $x$ independently with…
We consider a procedure to reduce simply generated trees by iteratively removing all leaves. In the context of this reduction, we study the number of vertices that are deleted after applying this procedure a fixed number of times by using…
A variety of algorithms have been proposed for reconstructing trees that show the evolutionary relationships between species by comparing differences in genetic data across present-day taxa. If the leaf-to-leaf distances in a tree can be…
We give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa. After the pairwise distances between terminal taxa are estimated from sequence data, the algorithm…
One can often make inferences about a growing network from its current state alone. For example, it is generally possible to determine how a network changed over time or pick among plausible mechanisms explaining its growth. In practice,…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
Historical linguistics aims at inferring the most likely language phylogenetic tree starting from information concerning the evolutionary relatedness of languages. The available information are typically lists of homologous (lexical,…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
We describe a technique to reorganize topologies of Steiner trees by exchanging neighbors of adjacent Steiner points. We explain how to use the systematic way of building trees, and therefore topologies, to find the correct topology after…
We study the problem of inferring network topology from information cascades, in which the amount of time taken for information to diffuse across an edge in the network follows an unknown distribution. Unlike previous studies, which assume…
In order to conduct a statistical analysis on a given set of phylogenetic gene trees, we often use a distance measure between two trees. In a statistical distance-based method to analyze discordance between gene trees, it is a key to decide…
We introduce the problem of isolating several nodes in random recursive trees by successively removing random edges, and study the number of random cuts that are necessary for the isolation. In particular, we analyze the number of random…