What is NP-hard optimization problems?
A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.
Can NP-hard problems be solved?
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 non-deterministic Algorithm/Turing Machine in polynomial time.
Which of the following gives a good solution to a NP-hard problems?
The first and most obvious approach to getting “pretty good” solutions to NP-Hard problems is to devise greedy algorithms. There are usually many possible greedy choices, some of which, like Dijkstra’s algorithm, can actually be quite sophisticated.
Which of following is NP-hard problem?
NP-complete problems are the hardest problems in the NP set. A decision problem L is NP-complete if: 1) L is in NP (Any given solution for NP-complete problems can be verified quickly, but there is no efficient known solution).
What are P and NP problems?
Roughly speaking, P is a set of relatively easy problems, and NP is a set that includes what seem to be very, very hard problems, so P = NP would imply that the apparently hard problems actually have relatively easy solutions.
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 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.
Which of the following is NP-hard problem?