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Very sharp transitions in one-dimensional MANETs
(2005)
We investigate how quickly phase transitions can occur in one-dimensional geometric random graph models of MANETs. In the case of graph connectivity, we show that the transition width behaves like 1/n (when the number n ...
A strong zero-one law for connectivity in one-dimensional geometric random graphs with non-vanishing densities
(2007)
We consider the geometric random graph where n points are distributed independently on the unit interval [0,1] according to some probability distribution function F. Two nodes communicate with each other if their distance ...
On the critical communication range under node placement with vanishing densities
(2007)
We consider the random network where n points are placed independently on the unit interval [0, 1] according to some probability distribution function F. Two nodes communicate with each other if their distance is less than ...
Connectivity in one-dimensional geometric random graphs: Poisson approximations, zero-one laws and phase transitions
(2008-10-24)
Consider n points (or nodes) distributed uniformly and independently on the unit interval [0,1]. Two nodes are said to be adjacent if their distance is less than some given threshold value.For the underlying random graph ...
On zero-one laws for connectivity in one-dimensional geometric random graphs
(2006)
We consider the geometric random graph where n points are distributed uniformly and independently on the unit interval [0,1]. Using the method of first and second moments, we provide a simple proof of the "zero-one" law ...