Related papers: On the Minimum Spanning Tree Distribution in Grids
Minimal spanning trees on infinite vertex sets are investigated. A criterion for minimality of a spanning tree having a finite length is obtained, which generalizes the corresponding classical result for finite sets. It is given an analytic…
A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…
The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant,…
We prove that any graph $G$ with $n$ points has a distribution $\mathcal{T}$ over spanning trees such that for any edge $(u,v)$ the expected stretch $E_{T \sim \mathcal{T}}[d_T(u,v)/d_G(u,v)]$ is bounded by $\tilde{O}(\log n)$. Our result…
We study the large-deviation properties of minimum spanning trees for two ensembles of random graphs with $N$ nodes. First, we consider complete graphs. Second, we study Erd\H{o}s-R\'{e}nyi (ER) random graphs with edge probability $p=c/N$…
We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $\delta$ of its edges must be different from those of the MST.…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
The main purpose of the paper is to develop an approach to evaluation or estimation of the spanning tree congestion of planar graphs. This approach is used to evaluate the spanning tree congestion of triangular grids.
Consider~\(n\) nodes distributed independently across~\(N\) cities contained with the unit square~\(S\) according to a distribution~\(f.\) Each city is modelled as an~\(r_n \times r_n\) square contained within~\(S\) and~\(MSTC_n\) denotes…
Among subgraphs with a fixed number of vertices of the regular square lattice, we prove inequalities that essentially say that those with smaller boundaries have larger numbers of spanning trees and vice-versa. As an application, we relate…
We obtain an exact formula for the probability that a uniformly random spanning tree of the $2$-by-$n$ square grid is ``balanced'' in the sense that it has an edge whose removal partitions its vertices into two sets of equal size. We…
A complete understanding of real networks requires us to understand the consequences of the uneven interaction strengths between a system's components. Here we use the minimum spanning tree (MST) to explore the effect of weight assignment…
The problem of spanning trees is closely related to various interesting problems in the area of statistical physics, but determining the number of spanning trees in general networks is computationally intractable. In this paper, we perform…
We study a new type of random minimum spanning trees. It is built on the complete graph where each vertex is given a weight, which is a positive real number. Then, each edge is given a capacity which is a random variable that only depends…
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in…
The fractal dimension of minimal spanning trees on percolation clusters is estimated for dimensions $d$ up to $d=5$. A robust analysis technique is developed for correlated data, as seen in such trees. This should be a robust method…
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…
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…
We consider the minimum spanning tree problem in a setting where the edge weights are stochastic from unknown distributions, and the only available information is a single sample of each edge's weight distribution. In this setting, we…