On the Length of a Random Minimum Spanning Tree

On the Length of a Random Minimum Spanning Tree

We study the expected value of the length Ln of the minimum spanning tree of the complete graph Kn when each edge e is given an independent uniform [0, 1] edge weight. We sharpen the result of Frieze [6] that limn→∞ E(Ln) = ζ(3) and show that E(Ln) = ζ(3) + c1 n + c2+o(1) n4/3 where c1, c2 are explicitly defined constants.

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...

A Note on Random Minimum Length Spanning Trees

Consider a connected r-regular n-vertex graph G with random independent edge lengths, each uniformly distributed on [0, 1]. Let mst(G) be the expected length of a minimum spanning tree. We show in this paper that if G is sufficiently highly edge connected then the expected length of a minimum spanning tree is ∼ nr ζ(3). If we omit the edge connectivity condition, then it is at most ∼ nr (ζ(3) +...

On the value of a random minimum length Steiner tree

Minimum Spanning Tree with Uncertain Random Weights

This paper considers the minimum spanning tree problem with uncertain random weights in an uncertain random network. The concept of uncertain random minimum spanning tree is initiated for minimum spanning tree problem with uncertain random edge weights. A model is presented to formulate a specific minimum spanning tree problem with uncertain random edge weights involving a distance chance distr...