What are some examples of NP problems?

Inhaltsverzeichnis:

1. What are some examples of NP problems?
2. What is the NP class problem?
3. Can NP problems be solved?
4. How do you prove a problem is NP?
5. Is there a problem in NP that is not NP-complete?
6. How do I know if I have NP-hard problems?
7. How do you show a problem is NP-hard?
8. How do you know if it is a NP problem?
9. How do you solve NP-hard problems?
10. How do I prove NP-hard reduction?
11. Why do we need to prove NP-completeness?
12. Is traveling salesman NP-hard?
13. Can you solve NP-hard problems?
14. Which type of problem may be NP-hard?
15. Is halting a problem with NP?
16. What happens if we prove P NP?

What are some examples of NP problems?

The list below contains some well-known problems that are NP-complete when expressed as decision problems.

• Boolean satisfiability problem (SAT)
• Knapsack problem.
• Hamiltonian path problem.
• Travelling salesman problem (decision version)
• Subgraph isomorphism problem.
• Subset sum problem.
• Clique problem.
• Vertex cover problem.

What is the NP class problem?

A problem is assigned to the NP (nondeterministic polynomial time) class if it is solvable in polynomial time by a nondeterministic Turing machine. A P-problem (whose solution time is bounded by a polynomial) is always also NP. A problem which is both NP and NP-hard is called an NP-complete problem. ...

Can NP problems be solved?

NP is set of decision problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. ... 1) L is in NP (Any given solution for NP-complete problems can be verified quickly, but there is no efficient known solution).

How do you prove a problem is NP?

A problem is “in NP” if, given a potential solution, you can verify that it is correct or incorrect in polynomial time. For instance if the problem is sorting lists, if you can verify that one list is the sorted version of another list in polynomial time, then sorting is in NP.

Is there a problem in NP that is not NP-complete?

Problems in NP not known to be in P or NP-complete Ladner showed that if P ≠ NP then there exist problems in NP that are neither in P nor NP-complete. Such problems are called NP-intermediate problems. ... If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level.

How do I know if I have NP-hard problems?

A problem X is NP-Complete if there is an NP problem Y, such that Y is reducible to X in polynomial time. NP-Complete problems are as hard as NP problems. A problem is NP-Complete if it is a part of both NP and NP-Hard Problem. A non-deterministic Turing machine can solve NP-Complete problem in polynomial time.

How do you show a problem 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.

How do you know if it is a NP problem?

A problem is NP if it is easy to verify a solution. It might not be easy to find such a solution, but given a candidate solution, we can easily verify whether it is in fact a solution or not. NP does not apply to algorithms, it applies to problems. A problem is NP if it is easy to verify a solution.

How do you solve NP-hard problems?

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 annon-deterministic Algorithm/Turing Machine in polynomial time. To solve this problem, do not have to be in NP .

How do I prove NP-hard reduction?

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.

Why do we need to prove NP-completeness?

Proving a problem NP-Complete is a research success because it frees you from having to search for an efficient and exact solution for the general problem you are studying.

Is traveling salesman NP-hard?

It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.

Can you solve NP-hard problems?

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 annon-deterministic Algorithm/Turing Machine in polynomial time. To solve this problem, do not have to be in NP .

Which type of problem may be NP-hard?

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.

Is halting a problem with NP?

- If we had a polynomial time algorithm for the halting problem, then we could solve the satisfiability problem in polynomial time using A and X as input to the algorithm for the halting problem . - Hence the halting problem is an NP-hard problem which is not in NP. - So it is not NP-complete.

What happens if we prove P NP?

If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers' problem-solving powers will remain fundamentally and permanently limited.