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Which problems are 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.
Is there any NP-complete optimization problems?
No optimization problems are NP-complete, as only decision problems are in NP. Optimization problems can have related decision problems that are in NP, and these related decision problems can be NP-complete.
Are all problems in NP NP-complete?
A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard. If some NP-complete problem has a polynomial time algorithm, all problems in NP do.
What is difference between NP-hard and NP-complete?
NP-Complete problems are as hard as NP problems….Difference between NP-Hard and NP-Complete:
| NP-hard | NP-Complete |
|---|---|
| To solve this problem, 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. |
Can P be reduced to NP complete?
Quick reply: No, it does not. Recall the definition of NP-hard problems. A problem X is NP-Hard if every problem in NP can be polynomially reduced to X. If on the other hand a problem X can be polynomially reduced to some NP-complete problem Y, it means that Y is at least as hard as X, not the other way around.
What does it mean if Q is NP-hard?
A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.
Can NP-hard be reduced to NP-complete?
(If P and NP are the same class, then NP-intermediate problems do not exist because in this case every NP-complete problem would fall in P, and by definition, every problem in NP can be reduced to an NP-complete problem.)
How are Ising spin glasses related to NP problems?
Analogies between the statistical physics of Ising spin glasses and NP problems have been frequently studied in the past [ 20 – 22 ], and have been used to construct simulated annealing algorithms [ 23] which have been quite fruitful in approximate algorithms for problems on classical computers.
Is the Ising model a NP complete model?
Mathematically, because the decision form of the Ising model is NP-complete, there exists a polynomial time mapping to any other NP-complete problem.
What does it mean when a problem is NP complete?
Mathematically, the fact that a problem is NP-complete means we can find a mapping to the decision form of the Ising model with a polynomial number of steps. This mapping can be re-interpreted as a pseudo-Boolean optimization problem [ 37 ].
How are spins used in the Ising model?
This collects and extends mappings to the Ising model from partitioning, covering, and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.