(definition)

**Definition:**
A minimum-weight *tree* connecting a designated set of *vertices*, called *terminals*, in an *undirected*, *weighted graph* or points in a space. The tree may include non-terminals, which are called *Steiner vertices* or *Steiner points*.

**Specialization** (... is a kind of me.)

*Euclidean Steiner tree*, *rectilinear Steiner tree*.

**See also**
*minimum spanning tree*.

*Note:
This differs from the minimum spanning tree in that the set of Steiner vertices must be identified. That is, additional vertices may be used. *

Named for Jakob Steiner.

* Some authors distinguish between Steiner trees and minimum Steiner trees.*

Author: JLG

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Entry modified 11 January 2010.

HTML page formatted Tue Dec 6 16:16:32 2011.

Cite this as:

Joseph L. Ganley, "Steiner tree", in
*Dictionary of Algorithms and Data
Structures* [online], Paul E. Black, ed.,
U.S. National Institute of
Standards and Technology. 11 January 2010. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/steinertree.html