Are NP-complete problems solved in polynomial time?

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Are NP-complete problems solved in polynomial time?

If an NP-complete problem can be solved in polynomial time then all problems in NP can be solved in polynomial time. If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.

Which of the following case does not exist in complexity theory?

1. Which of the following case does not exist in complexity theory? Explanation: Null case does not exist in complexity Theory.

What is not NP-complete?

7. No NP-complete problems are known to be in P. If there is a polynomial-time algorithm for any NP-complete problem, then P = NP, because any problem in NP has a polynomial-time reduction to each NP-complete problem.

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Is there a polynomial time algorithm for NP complete problems?

No polynomial time algorithm has yet been discovered for any NP complete problem, nor has anybody yet been able to prove that no polynomial-time algorithm exist for any of them. The interesting part is, if any one of the NP complete problems can be solved in polynomial time, then all of them can be solved.

What is the hardest problem in NP?

NP-complete problems are the hardest problems in NP set. A decision problem L is NP-complete if: 1) L is in NP (Any given solution for NP-complete problems can be verified quickly, but there is no efficient known solution). 2) Every problem in NP is reducible to L in polynomial time (Reduction is defined below).

What is the first NP-complete problem?

There must be some first NP-Complete problem proved by definition of NP-Complete problems. SAT (Boolean satisfiability problem) is the first NP-Complete problem proved by Cook (See CLRS book for proof).

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What is the difference between NP-hard and NP-completeness?

A problem is NP-Hard if it follows property 2 mentioned above, doesn’t need to follow property 1. Therefore, NP-Complete set is also a subset of NP-Hard set. NP-completeness applies to the realm of decision problems.