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askhelper's blog

Quarantine problem: Social distancing (NP?)
By askhelper, 4 years ago, In English

You are given an $$$N$$$x$$$N$$$ grid and $$$K$$$ people. Put all people in the grid such that the minimum manhattan distance between any two is maximized. What's the best solution for this problem? Is it NP?

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4 years ago, # |
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use binary search

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4 years ago, # |
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Is it manhattan or euclid distance?

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4 years ago, # |
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Deleted

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4 years ago, # |
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man if only someone could solve this

my first impression would be to fill in all 4 corners, then the middle, then the middle of each 4 resulting squares, then the 4 midpoints of each square, and keep on subdividing it until minimum

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    4 years ago, # ^ |
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    What if N = 4, and K = 16? Seems like greedy / binSearch solution would not be optimal here.

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4 years ago, # |
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NP contains decision problems. So you should also be given a value V and check if you can put the people in the grid so as their distances to satisfy the value V.

Now this problem is in NP because given a certificate (a placement of people) you can decide if this is a legal certificate or no in polynomial time. But this is easy.

Your actual question is if it is NP-complete, meaning if it has a polynomial time algorithm.

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