Low Degree Connectivity in Ad-Hoc Networks
The aim of the paper is to investigate the average case behavior of certain algorithms that are designed for connecting mobile agents in the two- or three-dimensional space. The general model is the following: let X be a set of points in the d-dimensional Euclidean space E d , d≥ 2; r be a function that associates each element of x ∈ X with a positive real number r(x). A graph G(X,r) is an oriented graph with the vertex set X, in which (x,y) is an edge if and only if ρ(x,y) ≤ r(x), where ρ(x,y) denotes the Euclidean distance in the space E d . Given a set X, the goal is to find a function r so that the graph G(X,r) is strongly connected (note that the graph G(X,r) need not be symmetric). Given a random set of points, the function r computed by the algorithm of the present paper is such that, for any constant δ, the average value of r(x) δ (the average transmitter power) is almost surely constant.
KeywordsPoisson Process Mobile Agent Open Site Giant Component Open Block
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- 3.Kleinrock, L., Silvester, J.A.: Optimum transmission radii for packet radio networks or why six is a magic number. In: IEEE Nat. Telecommun. Conf., pp. 431–435 (1978)Google Scholar
- 4.Peierls, R.: On Ising’s model of ferromagnetism. In: Proceedings of the Cambridge Philosophical Society, vol. 36, pp. 477–481Google Scholar