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The Steiner and Gromov–Steiner Ratios and Steiner Subratio in the Space of Compacta in the Euclidean Plane with Hausdorff Distance

Abstract

The Steiner and Gromov–Steiner ratios and Steiner subratio are fundamental characteristics of metric spaces. In this work, an attempt is made to find these ratios for the space of compacta in Euclidean space with Hausdorff metric.

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References

  1. 1.

    A. O. Ivanov and A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem,” Sb. Math., 203, No. 5, 677–726 (2012).

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Correspondence to Z. Ovsyannikov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 157–165, 2013.

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Ovsyannikov, Z. The Steiner and Gromov–Steiner Ratios and Steiner Subratio in the Space of Compacta in the Euclidean Plane with Hausdorff Distance. J Math Sci 203, 858–863 (2014). https://doi.org/10.1007/s10958-014-2177-4

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Keywords

  • Euclidean Space
  • Arbitrary Point
  • Minimal Span Tree
  • Fundamental Characteristic
  • HAUSDORFF Distance