Steiner Trees, Coordinate Systems and NP-Hardness

  • J. F. Weng
Part of the Combinatorial Optimization book series (COOP, volume 6)

Abstract

Given a set A of points a 1, a 2,..., in the Euclidean plane, the Steiner tree problem asks for a minimum network T(A) (or T if A is not necessarily mentioned) interconnecting A with some additional points to shorten the network [6]. The given points are referred to as terminals and the additional points are referred to as Steiner points. Trivially, T is a tree, called the Euclidean Steiner minimal tree (ESMT) for A. It is well known that Steiner minimal trees satisfy an angle condition: all angles at the vertices of Steiner minimal trees are not less than 120° [6]. A tree satisfying this angle condition is called a Steiner tree. Therefore, a Steiner minimal tree must be a Steiner tree.

Keywords

Steiner Tree Integer Point Steiner Point Steiner Tree Problem Negative Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • J. F. Weng
    • 1
  1. 1.Department of Mathematics and Statistics and Department of Electrical and Electronic EngineeringThe University of MelbourneParkvilleAustralia

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