Encyclopedia of Algorithms

Living Edition
| Editors: Ming-Yang Kao

Steiner Trees

Living reference work entry
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DOI: https://doi.org/10.1007/978-3-642-27848-8_403-2
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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...

Keywords and Synonyms

Approximation algorithm design 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer Science, University of Texas at DallasRichardson, TXUSA