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An Improved Approximation Algorithm for the Terminal Steiner Tree Problem

  • Yen Hung Chen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6784)

Abstract

Given a complete graph G = (V,E) with a length function on edges and a subset R of V, the terminal Steiner tree is defined to be a Steiner tree in G with all the vertices of R as its leaves. Then the terminal Steiner tree problem is to find a terminal Steiner tree in G with minimum length. In this paper, we present an approximation algorithm with performance ratio \(2\rho-\frac{(\rho\alpha^2-\alpha\rho)}{(\alpha+\alpha^2)(\rho-1)+2(\alpha-1)^2}\) for the terminal Steiner tree problem, where ρ is the best-known performance ratio for the Steiner tree problem with any α ≥ 2. When we let α = 3.87 ≈ 4, this result improves the previous performance ratio of 2.515 to 2.458.

Keywords

Approximation algorithms NP-complete Steiner tree terminal Steiner tree problem multicast routing evolutionary tree reconstruction in biology telecommunications 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yen Hung Chen
    • 1
  1. 1.Department of Computer ScienceTaipei Municipal University of EducationTaipeiTaiwan, R.O.C.

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