How to prove that a problem is NP complete?

Question

I have problem with scheduling. I need to prove that the problem is NP complete. What can be the methods to prove it NP complete?

Answer 1

In order to prove that a problem L is NP-complete, we need to do the following steps:

1. Prove your problem L belongs to NP (that is that given a solution you can verify it in polynomial time)
2. Select a known NP-complete problem L'
3. Describe an algorithm f that transforms L' into L
4. Prove that your algorithm is correct (formally: x ∈ L' if and only if f(x) ∈ L )
5. Prove that algo f runs in polynomial time