On the Value of a Random Minimum Weight Steiner Tree

A sharp threshold for minimum bounded-depth/diameter spanning and Steiner trees

In the complete graph on n vertices, when each edge has a weight which is an exponential random variable, Frieze proved that the minimum spanning tree has weight tending to ζ(3) = 1/13 + 1/23 + 1/33 + · · · as n → ∞. We consider spanning trees constrained to have depth bounded by k from a specified root. We prove that if k ≥ log2 log n+ω(1), where ω(1) is any function going to ∞ with n, then th...

On the value of a random minimum length Steiner tree

Solving a tri-objective convergent product network using the Steiner tree

Considering convergent product as an important manufacturing technology for digital products, we integrate functions and sub-functions using a comprehensive fuzzy mathematical optimization process. To form the convergent product, a web-based fuzzy network is considered in which a collection of base functions and sub-functions configure the nodes and each arc in the network is to be a link betwe...

(1 + ρ)-Approximation for Selected-Internal Steiner Minimum Tree

Selected-internal Steiner minimum tree problem is a generalization of original Steiner minimum tree problem. Given a weighted complete graph G = (V,E) with weight function c, and two subsets R ′ ( R ⊆ V with |R − R ′ | ≥ 2, selected-internal Steiner minimum tree problem is to find a Steiner minimum tree T of G spanning R such that any leaf of T does not belong to R ′ . In this paper, suppose c ...

Computing a Tree Having a Small Vertex Cover

We consider a new Steiner tree problem, called vertex-cover-weighted Steiner tree problem. This problem defines the weight of a Steiner tree as the minimum weight of vertex covers in the tree, and seeks a minimum-weight Steiner tree in a given vertex-weighted undirected graph. Since it is included by the Steiner tree activation problem, the problem admits an O(logn)-approximation algorithm in g...