What are the relationship among P NP NP complete and NP-hard problems?
NP-Complete problems are as hard as NP problems. A problem is NP-Complete if it is a part of both NP and NP-Hard Problem. A non-deterministic Turing machine can solve NP-Complete problem in polynomial time.
Is NP-hard harder than NP complete?
NP complete problem is both NP and NP-hard by definition. So NP-complete problems are not harder than NP problems – but they are as hard as least as any non-trivial problem in NP, and might be harder than P and NP-intermediate in case P≠NP.
Which problems can be NP complete?
NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.
What does NP stand for P vs NP?
P stands for polynomial time. NP stands for non-deterministic polynomial time.
What happens if we solve p np?
If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.
Can NP reduce to NP-hard?
Therefore, if any NP-complete problem has a polynomial time algorithm, then P = NP. See Figure 22.1 for the relation between P,NP,NP-complete and NP-hard. an NP-complete problem can be reduced to it; if we can do that, we know all problems in NP can be reduced to it by the definition of NP-hard.
Can P be NP-complete?
If any NP-complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.
Is P NP Decidable?
If P = NP, it is decidable. Because this states that there must be an algorithm for generating solutions in polynomial time.