Minimum Spanning Trees on Random Networks

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...

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) +...

Minimum spanning trees on polyhedra

In this paper, we consider the problem of generating a minimum spanning tree (MST) of a set of sites lying on the surface of an open polyhedron. The distance between any two sites is the length of a shortest path between them that is constrained to lie strictly upon the polyhedral surface. We present two algorithms, the first of which, when given m points on an n-faced polyhedron, produces an M...

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 ...