What is the difference between NP-hard and NP-complete problem?
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What is the difference between NP-hard and NP-complete problem?
A problem X is NP-Complete if there is an NP problem Y, such that Y is reducible to X in polynomial time….Difference between NP-Hard and NP-Complete:
| NP-hard | NP-Complete |
|---|---|
| To solve this problem, it do not have to be in NP . | To solve this problem, it must be both NP and NP-hard problems. |
| Do not have to be a Decision problem. | It is exclusively a Decision problem. |
Is NP-complete harder than NP-hard?
The polynomial-time reduction from your X to any problem in NP does not necessarily have a polynomial-time inverse. If the inverse is harder, then the verification is harder. An NP-complete problem, on the other hand, is one that is NP-hard and itself in NP.
Is NP-hard always NP-complete?
A NP-complete problem is a decision problem, which all NP problems can reduced to in polynomial time. They are the hardest problems in the class NP . The NP-hard class is the class of the problems which are at least as hard as the NP-complete problem.
What is NP-hard but not NP-complete?
The set of NP-hard problems is a superset of the set of NP-complete problems. There are complexity classes more “difficult” than NP, for example PSPACE, EXPTIME or EXPSPACE, and all these contain NP-hard but not NP-complete problems.
Is NP-hard subset of NP?
Therefore, the NP-Complete set is also a subset of the NP-Hard set. NP-completeness applies to the realm of decision problems. It was set up this way because it’s easier to compare the difficulty of decision problems than that of optimization problems.
Is AI NP-hard?
Much like in cryptography, NP-hardness doesn’t seem to capture the right notion of hardness for AI. Current AI systems have little trouble solving some kinds of NP-hard problems (large scheduling and planning problems, for example), but are totally clueless on solving others (how to compose a symphony, say).
What does NP-hard stand for?
In computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally “at least as hard as the hardest problems in NP”. A simple example of an NP-hard problem is the subset sum problem.
What is NP-hard in DAA?
A problem is NP-hard if all problems in NP are polynomial time reducible to it, even though it may not be in NP itself. If a polynomial time algorithm exists for any of these problems, all problems in NP would be polynomial time solvable. These problems are called NP-complete.
Why is TSP difficult NP?
Why TSP Is Not NP-complete Since it’s not in NP, it can’t be NP-complete. In TSP you’re looking for the shortest loop that goes through every city in a given set of cities. Since it takes exponential time to solve NP, the solution cannot be checked in polynomial time. Thus this problem is NP-hard, but not in NP.