相关论文: Variational Problems for Tree Roots and Branches
The root is an important organ of a plant since it is responsible for water and nutrient uptake. Analyzing and modelling variabilities in the geometry and topology of roots can help in assessing the plant's health, understanding its growth…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
This paper is aimed to investigate some computational aspects of different isoperimetric problems on weighted trees. In this regard, we consider different connectivity parameters called {\it minimum normalized cuts}/{\it isoperimteric…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…
Fruit tree image segmentation is an essential problem in automating a variety of agricultural tasks such as phenotyping, harvesting, spraying, and pruning. Many research papers have proposed a diverse spectrum of solutions suitable to…
Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree and the nervous or cardiovascular systems. Given a flow (traffic path)…
The structure of networks that provide optimal transport properties has been investigated in a variety of contexts. While many different formulations of this problem have been considered, it is recurrently found that optimal networks are…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…
In this paper we undertake a multiscale analysis of nutrient uptake by plant root hairs, considering different scale relations between the radius of hairs and the distance between them. We combine the method of formal asymptotic expansions…
The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
For rooted trees, an ideal drawing is one that is planar, straight-line, strictly-upward, and order-preserving. This paper considers ideal drawings of rooted trees with the objective of keeping the width of such drawings small. It is not…
Trees with many leaves have applications on broadcasting, which is a method in networks for transferring a message to all recipients simultaneously. Internal nodes of a broadcasting tree require more expensive technology, because they have…
A symbolic-computational algorithm, fully implemented in Maple, is described, that computes explicit expressions for generating functions that enable the efficient computations of the expectation, variance, and higher moments, of the random…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
We consider problems in which we are given a rooted tree as input, and must find a subtree with the same root, optimizing some objective function of the nodes in the subtree. When this function is the sum of constant node weights, the…
The Maximum (Minimum) Leaf Spanning Tree problem asks for a spanning tree with the largest (smallest) number of leaves. As spanning trees are often computed using graph search algorithms, it is natural to restrict this problem to the set of…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and…