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What is meant by NP-completeness?
NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.
What is P and NP-completeness?
What are NP, P, NP-complete and NP-Hard problems? P is 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-completeness applies to the realm of decision problems.
What is NP-completeness in automata?
A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) into p in polynomial time. It is not known whether every problem in NP can be quickly solved—this is called the P versus NP problem.
How do you determine NP-completeness of a problem?
Theorem If X is NP-complete, then X is solvable in polynomial time if and only if P = NP. Proof. If P = NP, then X can be solved in polytime. Suppose X is solvable in polytime, and let Y be any problem in NP.
Why do we need to prove NP completeness?
If you prove your problem to be NP-complete, then you have tied its hardness to the hardness of hundreds of other problems, each of significant interest to various communities. Thus, morally speaking, you can be assured that your problem is indeed hard.
What is an instance of NP complete problem?
The classic example of “NP-Complete” problems is the Traveling Salesman Problem. Imagine you need to visit 5 cities on your sales tour. You know all the distances.
Is chess NP complete or NP hard?
NP-complete is the hard parts of NP. Or, NP is superset of P and NP-complete. EXP is exponential. Not only is it ridiculously hard to solve, but also equally hard to check if your answer is correct. Like the best move in chess. NP-hard can be thought of as a super set of P, NP, and EXP.
What is NP algorithm?
An NP algorithm is an algorithm that has 2 stages: The first stage is a guessing stage that uses choose() to find a solution to the problem. The second stage checks the correctness of the solution produced by the first stage. The time of this stage is polynomial in the input size n. Template for an NP algorithm:
What is a NP problem?
An NP problem is an algorithmic problem such that if you have a case of the problem of size n {\\displaystyle n} , the number of steps needed to check the answer is smaller than the value of some polynomial in n {\\displaystyle n} .