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Steiner Trees

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

Years and Authors of Summarized Original Work

  • 2006; Du, Graham, Pardalos, Wan, Wu, Zhao

Definition

Given a set of points, called terminals, in a metric space, the problem is to find the shortest tree interconnecting all terminals. There are three important metric spaces for Steiner trees, the Euclidean plane, the rectilinear plane, and the edge-weighted network. The Steiner tree problems in those metric spaces are called the Euclidean Steiner tree (EST), the rectilinear Steiner tree (RST), and the network Steiner tree (NST), respectively. EST and RST have been found to have polynomial-time approximation schemes (PTAS) by using adaptive partition. However, for NST, there exists a positive number r such that computing r-approximation is NP-hard. So far, the best performance ratio of polynomial-time approximation for NST is achieved by k-restricted Steiner trees. However, in practice, the iterated 1-Steiner tree is used very often. Actually, the iterated 1-Steiner was proposed as a...

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Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan, Shanxi Province, China

    Weili Wu

  2. Department of Computer Science, California State University, Los Angeles, USA

    Weili Wu

  3. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  4. Department of Computer Science, The University of Texas at Dallas, Richardson, TX, USA

    Yaocun Huang

Authors
  1. Weili Wu
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  2. Yaocun Huang
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Wu, W., Huang, Y. (2016). Steiner Trees. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_403

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