- INSTANCE:
Graph
,
length function
,
set of sources ,
sink ,
demand function
,
finite set of cable types
where each cable type is specified by its capacity and its
cost per unit length.
- SOLUTION:
A network of cables in the graph, consisting of an integral number
of each cable type for each edge in
*G*, that routes all the demands at the sources to the sink. The demand of each source must follow a single path from source to sink. - MEASURE:
The total cost of building the network of cables.

*Good News:*Approximable within [49].*Comment:*Variations in which there are multiple sinks (a generalization of MINIMUM GENERALIZED STEINER NETWORK) or just a number*k*of the sources need to be connected to the sink (a generalization of MINIMUM*K*-STEINER TREE) is also approximable within [49]. Approximable within , where , for points in the Euclidean plane. Restricted version where the network to be designed must be a two-level tree (so that every path from a source to the sink consists of at most two edges) is approximable within [427].