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Node-placement based solutions strive to increase the sensor population close to
the sink in order to ensure the availability of spares. These spares will naturally
replace faulty nodes and thus sustain the network connectivity. Ishizuka and Aida [9]
have investigated random node distribution functions, trying to capture the faulttolerant
properties of stochastic placement. They have compared three deployment
patterns: simple diffusion (2-dimensional normal distribution), network configuration diagrams, and Rrandom,
where the nodes are uniformly scattered with respect to the radial and
angular directions from the sink. The R-random node distribution pattern resembles
the effect of an exploded shell and obeys the following probability density function
for sensor positions in polar coordinates
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