Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
I have two problems.
Is there a clique of size k in a graph? NP Hard
Is there a clique of size 50 in a graph? – Can be found out
in polynomial time O(n^50)
Why is the second problem not NP hard where as the first one is?
EDIT: Assuming P!=NP
The first problem is NP-hard because an arbitrary NP-complete problem (say, 3-SAT) can be reduced to it in polynomial time. (by the definition of NP-hardness)
The second problem is not NP-hard, because an arbitrary NP-complete problem cannot be reduced to it (say, 3-SAT, with >50 clauses).
In fact, the second problem is in P, because
O(n^50)belongs to P. But that isn’t the reason why it is not NP-hard (specifically, NP doesn’t mean non-polynomial).