Which type of problem may be NP-hard optimization or decision?

Another example of an NP-hard problem is the optimization problem of finding the least-cost cyclic route through all nodes of a weighted graph. This is commonly known as the travelling salesman problem. There are decision problems that are NP-hard but not NP-complete such as the halting problem.

How do you show that a problem is NP-complete?

We can solve Y in polynomial time: reduce it to X. Therefore, every problem in NP has a polytime algorithm and P = NP. then X is NP-complete. In other words, we can prove a new problem is NP-complete by reducing some other NP-complete problem to it.

What makes a problem NP-complete?

A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and all other NP problems are polynomial-time reducible to it, the problem is NP-complete.

What is the difference between NP-hard problems and NP-complete problems?

NP-Hard problems are as hard as NP-Complete problems. NP-Hard Problem need not be in NP class. 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.

How hard is the complexity class NP?

The complexity class NP is the class of decision problems where the ‘yes’ answers have short to state, quick to check proofs. Like COMPOSITE. One important point is that this definition doesn’t say anything about how hard the problem is. If you have a correct, efficient way to solve a decision problem,…

Do computers have P = NP problems?

It is largely believed that they do not. Here is an outstanding recent article on the latest (and the importance) of the P = NP problem: The Status of the P versus NP problem. The best book on the subject is Computers and Intractability by Garey and Johnson.

What is the best book on the P vs NP problem?

Here is an outstanding recent article on the latest (and the importance) of the P = NP problem: The Status of the P versus NP problem. The best book on the subject is Computers and Intractability by Garey and Johnson. I’ve been looking around and seeing many long explanations.