A Better Constant-Factor Approximation for Selected-Internal Steiner Minimum Tree

  • Authors:

  • Xianyue Li;Feng Zou;Yaochun Huang;Donghyun Kim;Weili Wu

  • Affiliations:

  • Lanzhou University, School of Mathematics and Statistics, 730000, Lanzhou, Gansu, P.R. China;University of Texas at Dallas, Department of Computer Science, 75080, Richardson, TX, USA;University of Texas at Dallas, Department of Computer Science, 75080, Richardson, TX, USA;University of Texas at Dallas, Department of Computer Science, 75080, Richardson, TX, USA;University of Texas at Dallas, Department of Computer Science, 75080, Richardson, TX, USA

  • Venue:
  • Algorithmica - Special Issue: Computation and Combinatorial Optimization; Guest Editors: Xiaodong Hu and Jie Wang
  • Year:
  • 2010

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Abstract

The 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 minimum subtree T of G interconnecting R such that any leaf of T does not belong to R ′. In this paper, suppose c is metric, we obtain a (1+ρ)-approximation algorithm for this problem, where ρ is the best-known approximation ratio for the Steiner minimum tree problem.