Approximating the selected-internal Steiner tree

(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 ...

Approximating Steiner trees

We give a presentation of Robins and Zelikovsky’s 1.55 approximation algorithm to the Steiner Tree Problem and a thorough proof of its approximation ratio. Furthermore we sketch a proof by Thimm bounding the approximability of the Steiner Tree Problem.

Approximating Full Steiner Tree in a Unit Disk Graph

Given an edge-weighted graph G = (V,E) and a subset R of V , a Steiner tree of G is a tree which spans all the vertices in R. A full Steiner tree is a Steiner tree which has all the vertices of R as its leaves. The full Steiner tree problem is to find a full Steiner tree of G with minimum weight. In this paper we present a 20-approximation algorithm for the full Steiner tree problem when G is a...

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...

Recent results on approximating the Steiner tree problem and its generalizations