Apr 21
traveling salesman is NP
Sam asked how a "proof certificate" for the traveling salesman problem works.
The answer is a bit tricky: the "decision" version of the the problem isn't
"find the minimum path", it's "is there a path shorter than a given distance L?"
The certificate is such a path; checking that it's shorter than L is trivial.
And the tricky part is that if you have a polynomial method for doing
the decision problem, then you can do a binary search on the possible
answer distances in polynomial time, thus solving the "find the minimum
path" problem in polynomial time.
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