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Encyclopedia of Algorithms pp 1–6Cite as

Rectilinear Steiner Tree

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Years and Authors of Summarized Original Work

  • 2003; Zhou

Problem Definition

Given n points on a plane, a Steiner minimal tree connects these points through some extra points (called Steiner points) to achieve a minimal total length. When the length between two points is measured by the rectilinear distance, the tree is called a rectilinear Steiner minimal tree.

Because of its importance, there is much previous work to solve the SMT problem. These algorithms can be grouped into two classes: exact algorithms and heuristic algorithms. Since SMT is NP-hard, any exact algorithm is expected to have an exponential worst-case running time. However, two prominent achievements must be noted in this direction. One is the GeoSteiner algorithm and implementation by Warme, Winter, and Zacharisen [14, 15], which is the current fastest exact solution to the problem. The other is a Polynomial Time Approximation Scheme (PTAS) by Arora [1], which is mainly of theoretical importance. Since exact...

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Recommended Reading

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  14. Warme DM, Winter P, Zacharisen M (2003) GeoSteiner 3.1 package. ftp://ftp.diku.dk/diku/users/martinz/geosteiner-3.1.tar.gz. Accessed Oct 2003

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Authors and Affiliations

  1. EECS Department, Northwestern University, Evanston, IL, USA

    Hai Zhou

Authors
  1. Hai Zhou
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Correspondence to Hai Zhou .

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Editors and Affiliations

  1. Dept. Electrical Engineering & Computer Science, Northwestern University, Evanston, Illinois, USA

    Ming-Yang Kao

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Zhou, H. (2015). Rectilinear Steiner Tree. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27848-8_337-2

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  • DOI: https://doi.org/10.1007/978-3-642-27848-8_337-2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Online ISBN: 978-3-642-27848-8

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