On the critical communication range under node placement with vanishing densities
On the critical communication range under node placement with vanishing densities
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Date
2007
Authors
Han, Guang
Makowski, Armand M.
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Makowski, Armand M.
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Abstract
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 some transmission range. When F admits a continuous density f with f = inf (f(x), x [0, 1]) > 0, it is known that the property of graph connectivity for the underlying random graph admits a strong critical threshold. Through a counterexample, we show that only a weak critical threshold exists when f = 0 and we identify it. Implications for the critical transmission range are discussed.