Can NP-complete problem be solved?

Can NP-complete problem be solved?

If some NP-complete problem has a polynomial time algorithm, all problems in NP do. The set of NP-complete problems is often denoted by NP-C or NPC. Although a solution to an NP-complete problem can be verified “quickly”, there is no known way to find a solution quickly.

What are steps to prove NP-completeness of a problem?

In order to prove that a problem L is NP-complete, we need to do the following steps:

• Prove your problem L belongs to NP (that is that given a solution you can verify it in polynomial time)
• Select a known NP-complete problem L’
• Describe an algorithm f that transforms L’ into L.

What are NP-complete problems and how do we solve them?

NP-Complete is a class of problems. The class P consists of those problems that are solvable in polynomial time. For example, they could be solved in O(nk) for some constant k, where n is the size of the input. Simply put, you can write a program that will run in reasonable time.

How many NP-complete problems are there?

This list is in no way comprehensive (there are more than 3000 known NP-complete problems). Most of the problems in this list are taken from Garey and Johnson’s seminal book Computers and Intractability: A Guide to the Theory of NP-Completeness, and are here presented in the same order and organization.

Which is not a characteristic of an NP-complete problem?

Which is not a characteristic of an NP-complete problem? No efficient algorithm has been found to solve an NP-complete problem. An efficient algorithm to solve an NP-complete problem may be possible. If an NP-complete problem has an efficient solution, then all NP-complete problems will have an efficient solution.

Why are NP-complete problems important?

NP-complete languages are significant because all NP-complete languages are thought of having similar hardness, in that process solving one implies that others are solved as well. If some NP-complete languages are proven to be in P, then all of NPs are proven to be in P.

How do you determine NP-complete?

We say X is NP-complete if: X ∈ NP • for all Y ∈ NP, Y ≤P X. If these hold, then X can be used to solve every problem in NP. Therefore, X is definitely at least as hard as every problem in NP.

What is the importance of NP-complete problem?

What is the difference between NP and NP-complete?

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….Difference between NP-Hard and NP-Complete: