Percolation thresholds on planar Euclidean relative-neighborhood graphs.

@article{Melchert2013PercolationTO,
  title={Percolation thresholds on planar Euclidean relative-neighborhood graphs.},
  author={Oliver Melchert},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={87 4},
  pages={
          042106
        }
}
  • O. Melchert
  • Published 29 January 2013
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
In the present article, statistical properties regarding the topology and standard percolation on relative neighborhood graphs (RNGs) for planar sets of points, considering the Euclidean metric, are put under scrutiny. RNGs belong to the family of "proximity graphs"; i.e., their edgeset encodes proximity information regarding the close neighbors for the terminal nodes of a given edge. Therefore they are, e.g., discussed in the context of the construction of backbones for wireless ad hoc… 

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References

SHOWING 1-10 OF 58 REFERENCES

Negative-weight percolation

We describe a percolation problem on lattices (graphs, networks), with edge weights drawn from disorder distributions that allow for weights (or distances) of either sign, i.e. including negative

Upper critical dimension of the negative-weight percolation problem.

This study investigates the geometric properties of loops on hypercubic lattice graphs in dimensions d=2 through 7, where edge weights are drawn from a distribution that allows for positive and negative weights, and finds numerical results consistent with an upper critical dimension d u=6 for the NWP problem.

Percolation thresholds, critical exponents, and scaling functions on planar random lattices and their duals.

  • H. HsuM. Huang
  • Mathematics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
It is demonstrated explicitly that the idea of a universal scaling function with nonuniversal metric factors in the finite-size scaling theory can be extended to random lattices and their duals for the existence probability, the percolating probability, and the mean cluster size.

Site percolation on planar Phi(3) random graphs.

  • J.-P. Kownacki
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
It is shown thatPercolation occurs for an occupation probability above a percolation threshold p(c) = 0.7360(5) .

Topology for efficient information dissemination in ad-hoc networking

A simulation of the information dissemination problem in ad-hoc wirless networks shows that the relative neighborhood graph has certain good graph properties, which makes it suitable for efficient information dissemination.

Critical Probabilities for Cluster Size and Percolation Problems

When particles occupy the sites or bonds of a lattice at random with probability p, there is a critical probability pc above which an infinite connected cluster of particles forms. Rigorous bounds

Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation.

  • C. Scullard
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2006
A correlated bond problem on the hexagonal lattice is solved by use of the star-triangle transformation and the site problem is solved, by a particular choice of correlations derived from a site-to-bond transformation, on the martini lattice.

Continuum Percolation Thresholds in Two Dimensions

  • S. MertensC. Moore
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
This work finds precise values of the percolation transition for disks, squares, rotated squares, and rotated sticks in two dimensions and confirms that these transitions behave as conformal field theory predicts.

Percolation threshold is not a decreasing function of the average coordination number.

  • J. Wierman
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2002
These counterexamples confirm the existence of this counterintuitive phenomenon, which was observed in one case in numerical estimates by van der Marck.
...