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
How do you prove a problem is NP-complete?
Suppose X is solvable in polytime, and let Y be any problem in NP. 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.
Are problems in P NP-complete?
NP-hard problems are those at least as hard as NP problems; i.e., all NP problems can be reduced (in polynomial time) to them. ... If any NP-complete problem is in P, then it would follow that P = NP . However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.
Can NP problems be solved?
If an NP-complete problem can be solved in polynomial time then all problems in NP can be solved in polynomial time. If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.
Which of the following problem is NP-complete?
Explanation: Hamiltonian circuit, bin packing, partition problems are NP complete problems.
What is NP-hard problem with example?
An example of an NP-hard problem is the decision subset sum problem : given a set of integers, does any non-empty subset of them add up to zero? That is a decision problem and happens to be NP-complete.
What does it mean if Q is NP-hard?
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.
What happens if P vs NP is solved?
If P equals NP, every NP problem would contain a hidden shortcut , allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.
What is N and P NP-complete problems?
P is a 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-complete problems are the hardest problems in the NP set.
Which type of problem may be NP-hard?
A problem is NP-hard if all problems in NP are polynomial time reducible to it , even though it may not be in NP itself. If a polynomial time algorithm exists for any of these problems, all problems in NP would be polynomial time solvable.
How do you solve NP-hard problems?
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 . To solve this problem, it do not have to be in NP .
Is chess an NP problem?
For two-player games, one encounters a similar phenomenon at a higher level of complexity. ... For this reason games like chess cannot themselves be NP-complete , as they only have a finite (albeit unthinkably large) number of possible positions.
Is Travelling salesman problem NP-complete?
Traveling Salesman Optimization(TSP-OPT) is a NP-hard problem and Traveling Salesman Search(TSP) is NP-complete . However, TSP-OPT can be reduced to TSP since if TSP can be solved in polynomial time, then so can TSP-OPT(1).
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).
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.
Why is knapsack problem NP hard?
the time needed increases in exponential term, so it’s a NPC problem. This is because the knapsack problem has a pseudo-polynomial solution and is thus called weakly NP-Complete (and not strongly NP-Complete).
