NP-Hard Vs. NP-Complete: Know the Difference Between NP-Hard and NP-Complete Problem
NP Problems are those sets of problems for which a typical user cannot find the solutions very easily. While finding solutions for an NP Problem is difficult- they are still very easy to verify. A Non-Deterministic Model can easily solve this type of problem in a given polynomial time. In this article, we will discuss the difference between NP-Hard and NP-Complete Problem. But let us understand their individual purposes in detail.
What is the NP-Hard Program?
Any given problem X acts as NP-Hard only if there exists a problem Y that is NP-Complete. Here, problem Y becomes reducible to problem X in a polynomial time. The hardness of an NP-Hard problem is equivalent to that of the NP-Complete Problem. But here, the NP-Hard Problems don’t need to be in the NP Class.
What is the NP-Complete Problem?
Any given problem X acts as NP-Complete when there exists an NP problem Y- so that the problem Y gets reducible to the problem X in a polynomial line. This means that a given problem can only become NP-Complete if it is a part of NP-Hard as well as NP Problems. A Turing machine of non-deterministic nature can easily solve this type of problem in a given polynomial time.
Difference Between NP-Hard and NP-Complete Problem
| Parameters | NP-Hard Problem | NP-Complete Problem |
| Meaning and Definition | One can only solve an NP-Hard Problem X only if an NP-Complete Problem Y exists. It then becomes reducible to problem X in a polynomial time. | Any given problem X acts as NP-Complete when there exists an NP problem Y- so that the problem Y gets reducible to the problem X in a polynomial line. |
| Presence in NP | The NP-Hard Problem does not have to exist in the NP for anyone to solve it. | For solving an NP-Complete Problem, the given problem must exist in both NP-Hard and NP Problems. |
| Decision Problem | This type of problem need not be a Decision problem. | This type of problem is always a Decision problem (exclusively). |
| Example | Circuit-satisfactory, Vertex cover, Halting problems, etc., are a few examples of NP-Hard Problems. | A few examples of NP-Complete Problems are the determination of the Hamiltonian cycle in a graph, the determination of the satisfaction level of a Boolean formula, etc. |
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