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How can we check a solution to the Traveling Salesman Problem

TakenItSeriously
in Computer Science

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Assume that you have discovered a method that can determine a very efficient route for any given set of cities every time, but your not sure if its the most efficient route.

How can we know if the resulting route is the most efficient? i.e. how can we test the method we have discovered to be the solution without actually solving all permutations for every problem?

Is their some formula that produces the minimum distance without giving the route?

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