(definition)

**Definition:**
For a given variant of the *Steiner tree* problem, the maximum possible ratio of the length of a *minimum spanning tree* of a set of *terminals* to the length of an optimal Steiner tree of the same set of terminals. Usually written ρ (rho).

*Note:
In graphs ρ = 2. In the Euclidean metric, ρ = 2/ √(3). In the rectilinear metric, ρ = 3/2.*

Author: JLG

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Entry modified 17 December 2004.

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Cite this as:

Joseph L. Ganley, "Steiner ratio", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: http://www.nist.gov/dads/HTML/steinerratio.html