"Springer-Verlag" . "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 $E_d$, $d\\ge 2$, $r$ be a function that associates each element of $x\\in X$ 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 $\\rho(x,y)\\le r(x)$, where $\\rho(x,y)$ 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). The function $r$ computed by the algorithm of the present paper is such that, given a random set $X$ of points, the average value of $r(x)^d$ (related to the average transmitter power) is almost surely constant." . "[0BC76A902E13]" . . . "Low degree connectivity in ad-hoc networks"@en . . . "2005-01-01+01:00"^^ . . "1"^^ . "11320" . . . "1"^^ . "12"^^ . . "Berlin" . "Berlin" . . . "000233893100020" . . "Low degree connectivity in ad-hoc networks" . "528450" . "Low degree connectivity in ad-hoc networks"@en . "3-540-29118-0" . . . "degree; connectivity; ad-hoc; networks"@en . "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 $E_d$, $d\\ge 2$, $r$ be a function that associates each element of $x\\in X$ 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 $\\rho(x,y)\\le r(x)$, where $\\rho(x,y)$ 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). The function $r$ computed by the algorithm of the present paper is such that, given a random set $X$ of points, the average value of $r(x)^d$ (related to the average transmitter power) is almost surely constant."@en . "Z(MSM0021620838)" . . . . "Ku\u010Dera, Lud\u011Bk" . "Low degree connectivity in ad-hoc networks" . "RIV/00216208:11320/05:00206154" . "RIV/00216208:11320/05:00206154!RIV10-MSM-11320___" . . "Algorithms - ESA 2005" .