What is np hard problem

What about P? P are problems which can be solved in Polynomial time. It is said that the problem is tractable , which means that the time a computer needs to solve your problem is normally not that long. NP means Nondeterministic Polynomial time. NP problems can't be solved in polynomial time by a computer means in a reasonable amount of time. However, it has never been proved, but it's highly suspected. If you have the solution of an NP problem, you could check if it solves the problem in reasonable amount of time; but the difficult part is to find the solution.

The major unsolved problem you speak about is: can you find a solution as quickly as you can verify if a solution solve a NP problem? If you can prove that yes, in that case we could solve NP problems easily. You'll be rich if you can do that. Adding to this, an NP-hard problem is a problem that is known to be at least as difficult to solve as the most difficult to solve problems in the NP complexity class.

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So I will try to contribute with an excellent resource about different classes of computational complexity. For someone who thinks that computational complexity is only about P and NP, here is the most exhaustive resource about different computational complexity problems.

Apart from problems asked by OP, it listed approximately different classes of computational problems with nice descriptions and also the list of fundamental research papers which describe the class.

As I understand it, an np-hard problem is not "harder" than an np-complete problem. In fact, by definition, every np-complete problem is:.

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Active Oldest Votes. Decision problem : A problem with a yes or no answer. Now, let us define those complexity classes. P P is a complexity class that represents the set of all decision problems that can be solved in polynomial time. Example Given a connected graph G , can its vertices be coloured using two colours so that no edge is monochromatic? NP NP is a complexity class that represents the set of all decision problems for which the instances where the answer is "yes" have proofs that can be verified in polynomial time.

Example Integer factorisation is in NP. Example 3-SAT. NP-hard Intuitively, these are the problems that are at least as hard as the NP-complete problems. Example The halting problem is an NP-hard problem. Improve this answer. We see that this algorithm halts if and only if I is satisfiable.

Thus, if we had a polynomial time algorithm for solving the halting problem then we could solve SAT in polynomial time. Therefore, the halting problem is NP-hard. Jason - You can't reduce a decidable problem to an undecidable problem in that manner. Decidable problems have to result in a definitive yes or no answer in order to be considered to be decidable. The Halting Problem does not have a definitive yes or now answer since an arbitrary answer might throw any solution into a loop.

Rob: Yes, I can. The definition of reducible does not require that the problem being reduced to be solvable. This is true for either many-one reductions or Turing reductions. Rob: Well, okay, if you want to continue this. First, "Decidable" is not synonomous with "decision problem" as you've used it.

Moreover, "decidable" can also be defined in terms of "computable functions. Using Halting problem as a "classic example" of NP-hard problem is incorrect. This is like saying: "Pacific Ocean is a classic example of a salt water aquarium. Show 22 more comments. The rest of NP hard is not. Johnson Wong Johnson Wong 3, 1 1 gold badge 13 13 silver badges 6 6 bronze badges. I've a doubt related to your answer. I asked it in a separate question, but I was asked to post it here. Can you please help me here?

It is unknown whether NP-complete problems are solvable in polynomial time. Also, NP-complete problems are NP-hard, so some NP-hard problems are verifiable in polynomial time, and possible some also polynomial-time solvable.