On the power assignment problem in radio networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
The number of neighbors needed for connectivity of wireless networks
Wireless Networks
Fast low degree connectivity of ad-hoc networks via percolation
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Wireless communication in random geometric topologies
ALGOSENSORS'06 Proceedings of the Second international conference on Algorithmic Aspects of Wireless Sensor Networks
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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 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 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.