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Probabilistic Properties of Topologies of Minimal Fillings of Finite Metric Spaces

Abstract

In this work, we provide a way to introduce a probability measure on the space of minimal fillings of finite additive metric spaces as well as an algorithm for its computation. The values of probability, obtained from the analytical solution, coincide with the computer simulation for the computed cases. Also the developed technique makes it possible to find the asymptotic of the ratio for families of graph structures.

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Correspondence to V. Salnikov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 2, pp. 181–196, 2013.

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Salnikov, V. Probabilistic Properties of Topologies of Minimal Fillings of Finite Metric Spaces. J Math Sci 203, 873–883 (2014). https://doi.org/10.1007/s10958-014-2179-2

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Keywords

  • Weight Distribution
  • Binary Tree
  • Boundary Vertex
  • Additive Space
  • Steiner Minimal Tree