| NP-Hard problems(say X) can be solved if and only if there is a NP-Complete problem(say Y) that can be reducible into X in polynomial time. |
NP-Complete problems can be solved by a non-deterministic Algorithm/Turing Machine in polynomial time. |
| 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. |
| Time is unknown in NP-Hard. |
Time is known as it is fixed in NP-Hard. |
| NP-hard is not a decision problem. |
NP-Complete is exclusively a decision problem. |
| Not all NP-hard problems are NP-complete. |
All NP-complete problems are NP-hard |
| Do not have to be a Decision problem. |
It is exclusively a Decision problem. |
| It is optimization problem used. |
It is Decision problem used. |
| Example: Halting problem, Vertex cover problem, etc. |
Example: Determine whether a graph has a Hamiltonian cycle, Determine whether a Boolean formula is satisfiable or not, Circuit-satisfiability problem, etc. |
