The Steiner Ratio of Neighboured Spaces
Let (X, ρ) be a metric space, and let (X′, ρ′) be a metric space that is “close” to (X, ρ). Then we may expect that a method to find a shortest tree in (X, ρ) can be extended to an approximate method in (X′, ρ′), and consequently, the Steiner ratios of the two spaces are not far from another. This is the main idea in the present chapter.
KeywordsUnit Ball Convex Body Positive Real Number Hausdorff Distance Steiner Point
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