What is the difference between P NP NP-hard and NP-complete?
A non-deterministic Turing machine can solve NP-Complete problem 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 the hardest?
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”. NP, it is unlikely that such an algorithm exists.
What is P NPC and NPH problems?
If any NPC Problem is polynomial time reducible to a problem X, that problem X belongs to NP-Hard class. Hence, all NP-Complete problems are also NPH. In other words if a NPH problem is non-deterministic polynomial time solvable, it is a NPC problem.
What is NP-hard and NP-complete problem?
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.
What is the hardest problem in NP?
NP-complete problems are the hardest problems in the NP set. A decision problem L is NP-complete if: 1) L is in NP (Any given solution for NP-complete problems can be verified quickly, but there is no efficient known solution). 2) Every problem in NP is reducible to L in polynomial time (Reduction is defined below).
How do you prove something is NP-hard?
To prove that problem A is NP-hard, reduce a known NP-hard problem to A. In other words, to prove that your problem is hard, you need to describe an ecient algorithm to solve a dierent problem, which you already know is hard, using an hypothetical ecient algorithm for your problem as a black-box subroutine.
What does it mean for a problem to be 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.
What do you mean by P NP and NP-hard problems explain giving examples?
P is a set of problems that can be solved by a deterministic Turing machine in Polynomial time. NP is set of decision problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. NP-complete problems are the hardest problems in the NP set.
