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I need to show that the Weighted Feedback Vertex Set (WFVS) is NP-Complete. How do I do this, I got confused. I'm not sure how to do this.

Thanks! :)

Boris Jakovljevic
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  • This sounds like a graph theory problem. I'd recommend moving your question to: http://mathoverflow.net/ or https://math.stackexchange.com/ – RutledgePaulV Jan 11 '15 at 23:17

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There are 3 basic steps to showing that a problem is in NP

  1. Decision Problem: Can you turn your problem into a decision problem? In the case of the WFVS problem, the decision problem might be "Given a graph G and real number K, is there a set of vertices V such that V satisfies the conditions of WFVS?
  2. Certificate: Can you identify an answer to your decision question? Again, in the case of the WFVS problem, an answer might be the set of vertices in the Graph
  3. Verification: Can you verify a certificate in polynomial time. By verifying in polynomial time, you know that the problem is not NP-Hard. Some verification steps might be: are all of the vertices/edges in the graph? is the sum of the weighted edges <= K? etc.

That is how you know that your problem is in NP.

NP Complete

To show that a problem is NP-Complete, you must find a commonly known NP-Complete problem, such as vertex cover or the travelling salesman problem, and show that your problem is just as hard as that problem by transforming the known problem into your problem, then proving that a 'yes' certificate to your problem implies a 'yes' certificate to the other problem, and vice versa.

This is how you show that your problem is NP-complete.

braedenrose
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