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Low Degree Connectivity in Ad-Hoc Networks

  • Luděk Kučera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3669)

Abstract

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 xX 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.

Keywords

Poisson Process Mobile Agent Open Site Giant Component Open Block 
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.

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References

  1. 1.
    Clementi, A., Penna, P., Silvestri, R.: On the Power Assignment Problem in Radio Networks. Mobile Networks and Applications 9, 125–140 (2004)CrossRefGoogle Scholar
  2. 2.
    Deuschel, J.-D., Pisztora, A.: Surface order large deviations fo high-density percolation. Probability Theory and Related Fields 104, 467–482 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 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. 4.
    Peierls, R.: On Ising’s model of ferromagnetism. In: Proceedings of the Cambridge Philosophical Society, vol. 36, pp. 477–481Google Scholar
  5. 5.
    Penrose, M.: Random Geometric Graphs. Oxford University Press, Oxford (2003)zbMATHCrossRefGoogle Scholar
  6. 6.
    Takagi, H., Kleinrock, L.: Optimal transmission ranges for randomly distributed packet radioterminals. IEEE Trans. Commun. COM-32, 246–257 (1984)CrossRefGoogle Scholar
  7. 7.
    Xue, F., Kumar, P.R.: The number of neighbors needed for connectivity of wireless networks. Wireless Networks 10, 169–181 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Luděk Kučera
    • 1
  1. 1.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

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