Find the smallest tree connecting all the vertices of T . Suppose we are given a set of sites that must be connected by wires as cheaply as possible. The minimum Steiner tree describes the way to connect them using the smallest amount of wire.
Analogous problems arise in designing networks of water pipes or heating ducts in buildings.
The Steiner tree problem is distinguished from the minimum spanning tree problem in that we are permitted to construct or select intermediate connection points to reduce the cost of the tree.