Steiner's problem in Euclid plane

Steiner's problem in Euclid plane --- евклидова задача Штейнера.

Let [math]\displaystyle{ P = \{p_{1}, p_{2}, \ldots, p_{n}\} }[/math] be a set of [math]\displaystyle{ n }[/math] given points (called terminal points) in the plane with a distance function [math]\displaystyle{ d }[/math]. A minimum cost network interconnecting these terminal points is called a Steiner minimal tree (SMT). The cost of a network is the sum of its edge costs and the cost of an edge is the distance (measured by the distance function [math]\displaystyle{ d }[/math]) between its end points. Therefore, an SMT is always a tree network whose leaf vertices are some of the terminal points and whose internal vertices are either terminal points or some Steiner points which are introduced to reduce the network cost. The Steiner's problem in Euclid plane or the Steiner tree problem asks for an SMT for a given set of terminal points with a given distance function. The Steiner tree problem with Euclidean and rectilinear distances attracted much attention due to their applications in telecommunications and in VLSI design of printed circuits.