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How do you know if you have a NP-hard problem?
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 version of a problem is used to determine if it is NP-hard?
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.
Are NP-hard problems solvable?
This is known as Cook’s theorem. What makes NP-complete problems important is that if a deterministic polynomial time algorithm can be found to solve one of them, every NP problem is solvable in polynomial time (one problem to rule them all).
Which of the following is not NP-hard?
Which of the following problems is not NP complete? Explanation: Hamiltonian circuit, bin packing, partition problems are NP complete problems.
How do you solve NP-complete problems?
Solving NP-complete problems
- Approximation: Instead of searching for an optimal solution, search for a solution that is at most a factor from an optimal one.
- Randomization: Use randomness to get a faster average running time, and allow the algorithm to fail with some small probability.
How do you determine a problem L is NP-complete explain with an example?
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). A problem is NP-Hard if it follows property 2 mentioned above, doesn’t need to follow property 1.
When is a problem an NP hard problem?
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. A problem is NP-Complete if it is a part of both NP and NP-Hard Problem.
Can a NP hard problem be solved in polynomial time?
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.
Is the graph partitioning problem NP hard or NP complete?
If only a subset of the nodes has to be transferred then this is a graph partitioning problem known: partitioning the vertices of a graph into two subsets such that the weight of the cut between the two subsets is minimum. It was proved NP-hard; the proof is given in the famous Garey & Johnson’s book on computational complexity theory.
Can a non deterministic Turing machine solve a NP hard problem?
A non-deterministic Turing machine can solve NP-Complete problem in polynomial time. 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.