Related papers: Spectral ordering and 2-switch transformations
We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The…
The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…
Given an undirected graph $G$ whose edge weights change over $s$ time slots, the sub-tree scheduling for wireless sensor networks with partial coverage asks to partition the vertices of $G$ in $s$ non-empty trees such that the total weight…
The overlap graphs of subtrees in a tree (SOGs) generalise many other graphs classes with set representation characterisations. The complexity of recognising SOGs in open. The complexities of recognising many subclasses of SOGs are known.…
A spanning tree of a graph $G$ is a connected acyclic spanning subgraph of $G$. We consider enumeration of spanning trees when $G$ is a $2$-tree, meaning that $G$ is obtained from one edge by iteratively adding a vertex whose neighborhood…
Using the existence of a good leaf in every simplicial tree, we order the facets of a simplicial tree in order to find combinatorial information about the Betti numbers of its facet ideal. Applications include an Eliahou-Kervaire splitting…
We arrange the orders in an algebraic number field in a tree. This tree can be used to enumerate all orders of bounded index in the maximal order as well as the orders over some given order.
Degree assortativity refers to the increased or decreased probability of connecting two neurons based on their in- or out-degrees, relative to what would be expected by chance. We investigate the effects of such assortativity in a network…
A semiregular tree is a tree where all non-pendant vertices have the same degree. Belardo et al. (MATCH Commun. Math. Chem. 61(2), pp. 503-515, 2009) have shown that among all semiregular trees with a fixed order and degree, a graph with…
An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of…
Species tree estimation is a complex problem, due to the fact that different parts of the genome can have different evolutionary histories than the genome itself. One of the causes for this discord is incomplete lineage sorting (also called…
The seriation problem seeks to reorder a set of elements given pairwise similarity information, so that elements with higher similarity are closer in the resulting sequence. When a global ordering consistent with the similarity information…
The wavelet transform has seen success when incorporated into neural network architectures, such as in wavelet scattering networks. More recently, it has been shown that the dual-tree complex wavelet transform can provide better…
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…
We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…
This paper presents two approaches to quantifying and visualizing variation in datasets of trees. The first approach localizes subtrees in which significant population differences are found through hypothesis testing and sparse classifiers…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
Perfect sorting by reversals, a problem originating in computational genomics, is the process of sorting a signed permutation to either the identity or to the reversed identity permutation, by a sequence of reversals that do not break any…
A tree $T$ on $2^n$ vertices is called set-sequential if the elements in $V(T)\cup E(T)$ can be labeled with distinct nonzero $(n+1)$-dimensional $01$-vectors such that the vector labeling each edge is the component-wise sum modulo $2$ of…
Spanning trees of complete bipartite graphs exhibit a rich interaction between degree sequences and graph structure. In this paper, we obtain lower bounds on the number of isomorphism classes of spanning trees in $K_{a,b}, 2 \leq a \leq b$…