Advances in Steiner Trees pp 63-80 | Cite as

# Steiner Trees, Coordinate Systems and NP-Hardness

## 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## Preview

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