Steiner ratio is a characteristic of metric space estimating possible relative error of approximation of a shortest tree for a finite subset of the metric space by minimal spanning tree in the worst possible case. This characteristic of metric spaces is actively studied since 1960th. The paper presents recent results in the subject (for 2002), in particular, gaps in Du and Hwang work on Gilbert—Pollack conjecture on Steiner ratio of Euclidean plane are discussed.

Steiner problem, Steiner ratio, shortest network, minimal spanning tree

Mathematical problems and theory of numerical methods