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I have a semi-circle on a plane and I need to determine the point on such semicircle that maximizes the sum of distances to N given points. I'm wondering what algorithm would be suitable for solving this problem efficiently. Also an approximated solution is fine.

Any suggestions or guidance would be greatly appreciated. Thank you!

Daniele Affinita
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  • This problem is hard. Are you sure you need exactly this? Maximizing or minimizing the sum of the squared distances is super easy. – Matt Timmermans Jun 25 '23 at 16:22
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    I would "brute force" it by [Approximation search](https://stackoverflow.com/a/36163847/2521214) its just single search through angle ... so speed is not an issue here unless the number of points is huge – Spektre Jun 26 '23 at 06:11
  • Thanks, @Spektre. I think I'm going to use your suggestion. Indeed usually N = 6 at most so I can apply an approximation search – Daniele Affinita Jun 26 '23 at 08:14

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