True or False: If an NP-complete problem can be solved in cubic time, then all NP...
True or False: If an NP-complete problem can be solved in cubic time, then all NP complete problems can be solved in cubic time. Cubic = O(n^3). Explain why true or false. I think the answer is False but I'm not exactly sure why that is so if someone could explain.
Homework Answers
False:
A problem x that is in NP is also in NP-Complete if and only if every other problem in NP can be quickly (ie. in polynomial time) transformed into x.
In other words:
- x is in NP, and
- Every problem in NP is reducible to x
Now, in order for every problem to be solved in cubic time, they need to be polynomially reduced to the NP-complete problem x (which can be solved in polynomial time) which is not always true.
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