Advertisement

Journal of Mathematical Sciences

, Volume 203, Issue 6, pp 873–883 | Cite as

Probabilistic Properties of Topologies of Minimal Fillings of Finite Metric Spaces

  • V. SalnikovEmail author
Article
  • 31 Downloads

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.

Keywords

Weight Distribution Binary Tree Boundary Vertex Additive Space Steiner Minimal Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Y. Eremin, “A formula for the weight of a minimal filling of a finite metric space,” Sb. Math., 204, No. 9, 1285–1306 (2013).CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    M. R. Garey, R. L. Graham, and D. S. Johnson, “The complexity of computing Steiner minimal trees,” SIAM J. Appl. Math., 32, 835–859 (1977).CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    M. Gromov, “Filling Riemannian manifolds,” J. Differ. Geom., 18, 1–147 (1983).zbMATHMathSciNetGoogle Scholar
  4. 4.
    A. O. Ivanov and A. A. Tuzhilin, Extreme Networks Theory [in Russian], Inst. Komp’yut. Issled., Moscow, Izhevsk (2003).Google Scholar
  5. 5.
    A. O. Ivanov and A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem,” Sb. Math., 203, No. 5, 677–726 (2012).CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    R. M. Karp, “Reducibility among combinatorial problems,” in: R. E. Miller and J. W. Thatcher, eds., Complexity of Computer Computations: Proc. of a Symp. on the Complexity of Computer Computations, IBM Res. Symp. Ser., Plenum, New York (1972), pp. 85–103.Google Scholar
  7. 7.
    Z. N. Ovsyannikov, “Generalized additive spaces,” in press.Google Scholar
  8. 8.
    K. A. Zareckiy, “Constructing a tree on the basis of a set of distances between the hanging vertices,” Usp. Mat. Nauk, 20, No. 6, 90–92 (1965).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Yaroslavl State University, Delone Laboratory of Discrete and Computational GeometryYaroslavlRussia

Personalised recommendations