We investigate Prim’s standard ‘tree-growing’ method for finding a minimum spanning tree, when applied to a network in which all degrees are about d and the edges e have independent identically distributed random weights w(e). We find that when the kth edge ek is added to the current tree, where k = o( √ d), the probability that this edge ek is incident to the node that was most recently added ...

The Standard Hough Transform (SHT) is used to find lines, circles and other image features in edge maps containing edge points. Edge points which potentially can ‘vote’ for a given line (called its ‘line support’) are highly dependent of line position and orientation due to the boundedness of images. If accumulator array peaks are used to find lines then peripherally located lines are missed. U...

The existence of (shortest-path) interval routing schemes for random graphs that use at most one interval label per edge is an open problem posed in [8]. In this paper, we show that for any random graph G(n, p) with edge probability p > 0.765, there exists an interval routing scheme that uses at most one label per edge and has an additive stretch 1. In doing so, we provide an interesting constr...

let $d$ be a digraph with vertex set $v(d)$. for vertex $vin v(d)$, the degree of $v$,denoted by $d(v)$, is defined as the minimum value if its out-degree and its in-degree.now let $d$ be a digraph with minimum degree $deltage 1$ and edge-connectivity$lambda$. if $alpha$ is real number, then the zeroth-order general randic index is definedby $sum_{xin v(d)}(d(x))^{alpha}$. a digraph is maximall...

An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the inverse minimum spanning tree problem with stochastic edge weights is investigated. The concept of α-minimum spanning tree is initiated, and subsequently an α-minimum spanning tr...

We consider the problem of finding shortest paths in a graph with independent randomly distributed edge lengths. Our goal is to maximize the probability that the path length does not exceed a given threshold value (deadline). We give a surprising exact n n) algorithm for the case of normally distributed edge lengths, which is based on quasi-convex maximization. We then prove average and smoothe...

A theory of the probability distribution function (PDF) tails of the blob density in plasma edge turbulence is provided. A simplified model of the fast convective radial transport is used. The theoretically predicted PDF tails corroborate earlier measurements of edge transport, further confirming the strongly non-Gaussian feature of edge transport. It is found that increasing the cross sectiona...

This paper introduces a multi-view recurrent neural network (MV-RNN) approach for 3D mesh segmentation. Our architecture combines the convolutional neural networks (CNN) and a two-layer long short term memory (LSTM) to yield coherent segmentation of 3D shapes. The imaged-based CNN are useful for effectively generating the edge probability feature map while the LSTM correlates these edge maps ac...

Consider the complete n-graph with independent exponential (mean n) edge-weights. Let M (c; n) be the maximal size of subtree for which the average edge-weight is at most c. It is shown that M (c; n) transitions from o(n) to (n) around some critical value c(0), which can be speciied in terms of a xed point of a mapping on probability distributions .

We consider the discrete Laplace operator ∆ on Erdős–Rényi random graphs with N vertices and edge probability p/N . We are interested in the limiting spectral properties of ∆ as N → ∞ in the subcritical regime 0 < p < 1 where no giant cluster emerges. We prove that in this limit the expectation value of the integrated density of states of ∆ exhibits a Lifshits-tail behaviour at the lower spectr...