Related papers: A rearrangement distance for fully-labelled trees
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
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…
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…
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,…
A widely used method for determining the similarity of two labeled trees is to compute a maximum agreement subtree of the two trees. Previous work on this similarity measure is only concerned with the comparison of labeled trees of two…
An ordered labeled tree is a tree in which the nodes are labeled and the left-to-right order among siblings is relevant. The edit distance between two ordered labeled trees is the minimum cost of changing one tree into the other through a…
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…
Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
We describe a kernel of size 9k-8 for the NP-hard problem of computing the Tree Bisection and Reconnect (TBR) distance k between two unrooted binary phylogenetic trees. We achieve this by extending the existing portfolio of reduction rules…
We study the problem of learning a node-labeled tree given independent traces from an appropriately defined deletion channel. This problem, tree trace reconstruction, generalizes string trace reconstruction, which corresponds to the tree…
Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First,…
Rotation distance between rooted binary trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. We give an efficient,…
CONTEXT. Attack treesare a recommended threat modeling tool, but there is no established method to compare them. OBJECTIVE. We aim to establish a method to compare "real" attack trees, based on both the structure of the tree itself and the…
The problem of reconstructing evolutionary trees or phylogenies is of great interest in computational biology. A popular model for this problem assumes that we are given the set of leaves (current species) of an unknown binary tree and the…
Given two messages - as linear sequences of letters, it is immediate to determine whether one can be transformed into the other by simple substitution cipher of the letters. On the other hand, if the letters are carried as labels on nodes…
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…
This paper provides a short and transparent solution for the covering cost of white-grey trees which play a crucial role in the algorithm of Bergeron {\it et al.}\ to compute the rearrangement distance between two multichromosomal genomes…
In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…