Low Degree Connectivity in Ad-Hoc Networks

  • Luděk Kučera
Conference paper
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 Ed, 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 Ed. 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.

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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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