Travelling Salesman

  • Thread starter Dragonfall
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  • #1
Dragonfall
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I don't understand how travenlling salesman is NP-complete. In particular, how can you possibly verify that a given route is the shortest one in polynomial time?
 

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  • #2
daniel_i_l
Gold Member
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The TSP isn't NP-complete - it's NP-hard. But the question: Is there a path shorter than x is NP-complete. A problem is NP-hard iff it can be used to solve an NP-complete problem in O(n) time.
 
Last edited:
  • #3
PowerIso
329
1
TSP is only NP-complete if you use the decision version of the problem.

Side note, TSP is one reason why combinatorial optimization is one of my favorite subjects.
 
  • #4
Dragonfall
1,030
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This makes a lot more sense.
 

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