# Packing of nodes in a circle

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.

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Related question: math.stackexchange.com/questions/118265/… – Joachim Breitner Dec 15 '12 at 14:10
@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). – kashyap1123 Jan 19 '13 at 20:18
Probably not directly, I was just adding pointers for the passing by reader. – Joachim Breitner Jan 19 '13 at 21:13

I doubt very much that there is a closed-form solution. Packing problems tend to be hard. You might be able to get upper and lower bounds.

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I should've asked for this in the question. Will add. Thank you ! – kashyap1123 Oct 30 '12 at 6:26