Routing in Poisson small-world networks

Details Routing in Poisson small-world networks Routing in Poisson small-world networks

2005-08-22

arxiv.org/abs/math/0508410v1

Mathematics

Probability

8 pages

Scientific paper

In recent work, Jon Kleinberg considered a small-world network model consisting of a d-dimensional lattice augmented with shortcuts. The probability of a shortcut being present between two points decays as a power of the distance between them. Kleinberg studied the efficiency of greedy routing depending on the value of the power. The results were extended to a continuum model by Franceschetti and Meester. In our work, we extend the result to more realistic models constructed from a Poisson point process, wherein each point is connected to all its neighbours within some fixed radius, as well as possessing random shortcuts to more distant nodes as described above.

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