相关论文: Minimum spanning trees on random networks

We show that the diameter of a uniformly drawn spanning tree of a simple connected graph on $n$ vertices with minimal degree linear in $n$ is typically of order $\sqrt{n}$. A byproduct of our proof, which is of independent interest, is that…

A classical result by Otter shows that the complete graph has an exponential number of non-isomorphic spanning trees. This was recently extended by Lee to every almost regular graph of sufficiently large degree. In this paper, we consider…

We show that the Brownian continuum random tree is the Gromov-Hausdorff-Prohorov scaling limit of the uniform spanning tree on high-dimensional graphs including the $d$-dimensional torus $\mathbb{Z}_n^d$ with $d>4$, the hypercube…

The run time complexity of state-of-the-art inference algorithms in graph-based dependency parsing is super-linear in the number of input words (n). Recently, pruning algorithms for these models have shown to cut a large portion of the…

We consider the minimum spanning tree (MST) problem under the restriction that for every vertex v, the edges of the tree that are adjacent to v satisfy a given family of constraints. A famous example thereof is the classical…

In 1985, Frieze showed that the expected sum of the edge weights of the minimum spanning tree (MST) in the uniformly weighted graph converges to $\zeta(3)$. Recently, Hino and Kanazawa extended this result to a uniformly weighted simplicial…

It is well known that finding extremal values and structures can be hard in weighted graphs. However, if the weights are random, this problem can become way easier. In this paper, we examine the minimal weight of a union of $k$…

We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties…

We give a simple deterministic constant-round algorithm in the congested clique model for reducing the number of edges in a graph to $n^{1+\varepsilon}$ while preserving the minimum spanning forest, where $\varepsilon > 0$ is any constant.…

Let $P$ be a generic set of $n$ points in the plane, and let $P=R\cup B$ be a coloring of $P$ in two colors. We are interested in the number of crossings between the minimum spanning trees (MSTs) of $R$ and $B$, denoted by $\crossAB(R,B)$.…

Computing a Euclidean minimum spanning tree of a set of points is a seminal problem in computational geometry and geometric graph theory. We combine it with another classical problem in graph drawing, namely computing a monotone geometric…

We show optimal lower bounds for spanning forest computation in two different models: * One wants a data structure for fully dynamic spanning forest in which updates can insert or delete edges amongst a base set of $n$ vertices. The sole…

The seeded Watershed algorithm / minimax semi-supervised learning on a graph computes a minimum spanning forest which connects every pixel / unlabeled node to a seed / labeled node. We propose instead to consider all possible spanning…

Study of random networks generally requires the nodes to be independently and uniformly distributed such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a…

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid…

We present a self-stabilizing protocol for an overlay network that constructs the Minimum Spanning Tree (MST) for an underlay that is modeled by a weighted tree. The weight of an overlay edge between two nodes is the weighted length of…

We construct forests that span $\mathbb{Z}^d$, $d\geq2$, that are stationary and directed, and whose trees are infinite, but for which the subtrees attached to each vertex are as short as possible. For $d\geq3$, two independent copies of…

For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…

Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…

Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…