## Abstract

Suppose *A* = {*a* _{l}, *a* _{2}, ... , *a* _{ n }} is a point set in a metric space **M**. The shortest network problem asks for a minimum length network *S*(*A*) that interconnects all points of *A* (called *terminals*), possibly with some additional points to shorten the network. *S*(*A*) must be a tree since it cannot contain any cycle for minimality. In the literature this problem is called the *Steiner tree problem*, and *S*(*A*) is called a *Steiner minimal tree* for *A* [9]. If no additional points are added, then the network, denoted by *T*(*A*), is called a *minimal spanning tree* on *A*. Sometimes these networks are simply denoted by *S* and *T* if no confusion is caused.

## Keywords

Minimal Span Tree Steiner Tree Euclidean Plane Steiner Point Steiner Tree Problem
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