Article collection "Mathematical Problems of Cybernetics" №16, Moscow, 2007

Authors:Ivanov A.O., Tuzhilin A.A.

Uniqueness of the shortest tree spanning a boundary in general position in the plane

Abstract:

In the paper the following result is presented: there exists an open everywhere dense subset U⊂R^{2n}, such that any P∈U considered as an enumerated n-element subset of the standard Euclidean plane, is connected by unique Steiner minimal tree, i.e., a non-degenerate shortest tree.

Keywords:

Steiner problem, shortest tree, minimal network, Steiner minimal tree

Publication language:russian,
pages:8(p. 155-162)

Research direction:

Mathematical problems and theory of numerical methods