Minimum spanning trees and random resistor networks inddimensions

On random minimum lenght spanning trees

On Random Minimum Length Spanning Trees

Suppose that we are given a complete graph K n on n vertices together with lengths on the edges which are independent identically distributed non-negative random variables. Suppose that their common distribution function F satisfies F(0) =0, F is differentiable from the right at zero and D = F~. (0)>0. Let X denote a random variable with this distribution. Let L~ denote the (random) length of t...

Minimum congestion spanning trees in bipartite and random graphs

The first problem considered in this paper: is it possible to find upper estimates for the spanning tree congestion for bipartite graphs which are better than for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n 3 2 , where n is the number of vertices. The second problem is to estimate spanning tree congestion of rand...

Geometric Minimum Spanning Trees

Let S be a set of n points in < d. We present an algorithm that uses the well-separated pair decomposition and computes the minimum spanning tree of S under any Lp or polyhedral metric. It has an expected running time of O(n logn) for uniform distributions. Experimentalresults show that this approachis practical. Under a variety of input distributions, the resultingimplementation is robust and ...

Minimum Spanning Trees∗

1 Background Members of some secret party want to shutdown some high risk communication channals, while preserving low risk channals to ensure that members are still connected in the secret network.