On the internal steiner tree problem

Authors:
Sun-Yuan Hsieh;Huang-Ming Gao;Shih-Cheng Yang
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

Citing 5
Cited 0

Optimization, approximation, and complexity classes

STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
The steiner problem with edge lengths 1 and 2,

Information Processing Letters
Introduction to algorithms

Introduction to algorithms
Proof verification and the hardness of approximation problems

Journal of the ACM (JACM)
Improved Steiner tree approximation in graphs

SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a complete graph G = (V,E) with a cost function c : E → R+ and a vertex subset R ⊂ V, an internal Steiner tree is a Steiner tree which contains all vertices in R such that each vertex in R is restricted to be an internal vertex. The internal Steiner tree problem is to find an internal Steiner tree T whose total costs Sigma;(u,v)isin;E(T) c(u, v) is minimum. In this paper, we first show that the internal Steiner tree problem is MAX SNP-hard. We then present an approximation algorithm with approximation ratio 2ρ + 1 for the problem, where ρ is the best known approximation ratio for the Steiner tree problem.