This is in a scenario of packing wireless transmitters in a circle with interference constraints. We would like to place $N$ nodes, transmitting at a fixed power $P_{T}$ in a circle of radius $R$. Each encounters interference from the $N-1$ others as per the power law: $$ P_{Int,i} = \sum_{j \neq i} P_{T}d_{ij}^{-\alpha} $$ where $d_{ij}$ is the distance between nodes $i$ and $j$. $\alpha$ is the path-loss exponent (usually between 2 and 4). What is the maximum number of nodes that can be placed in the circle, while obeying the interference constraint: $$ P_{Int,i} \leq P_{Thresh} $$ or, if there are any closed-form bounds on the answer.
Packing of nodes in a circle
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geometry
packing-problem
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0Related question: http://math.stackexchange.com/questions/118265/circle-packing-algorithm – 2012-12-15
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0@JoachimBreitner Thanks for the link. I am not sure how this problem would translate into the packing of circles (except for a trivial bound, I am not sure how else). – 2013-01-19
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0Probably not directly, I was just adding pointers for the passing by reader. – 2013-01-19