Suppose I have a large square and a set of $n$ circles, each with a different radius $r$, such that there exists some way to fit all the circles into the square. Is there an algorithm to find the "best" arrangement of the circles in the square, so that none of the circles overlap and there is the most amount of space possible between them?

(Note that I don't mean a regular circle-packing algorithm, where the circles are all the same size like in the image.)

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(PS: sorry if it's unclear, I have a fixed, constant size of the square and a finite set of unequal circles. I'm not trying to minimize anything, just find the best way to arrange these circles without using a brute-force method)

  • $\begingroup$ If you want to find the “best” arrangement, that means you’re trying to minimize (or maximize) something. You say you want to arrange the circles so that there is “the most amount of space possible between them” which sounds like you’re maximizing something. How do you define the space between them? $\endgroup$ – David M. Mar 15 at 8:21

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