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What is NP and NP-hard problem?

Diana Montgomery2019-07-13

What is NP and NP-hard problem?

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. These problems are called NP-complete.

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.

Is NP-hard harder than NP?

An NP-hard problem can be beyond NP. The polynomial-time reduction from your X to any problem in NP does not necessarily have a polynomial-time inverse. If the inverse is harder, then the verification is harder. An NP-complete problem, on the other hand, is one that is NP-hard and itself in NP.

Can 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.

What is NP-hard problem in algorithm?

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 are NP class problems?

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 are polynomial-time reducible to it, the problem is NP-complete.

What does NP mean in math?

nondeterministic polynomial time
NP (which stands for nondeterministic polynomial time) is the set of problems whose solutions can be verified in polynomial time. But as far as anyone can tell, many of those problems take exponential time to solve.

Which of the 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). 2) Every problem in NP is reducible to L in polynomial time (Reduction is defined below).

Users' questions

What is NP and NP hard problem?

Diana Montgomery2019-06-06

What is NP and NP hard problem?

Is chess NP-hard?

As a decision problem, it’s complexity is characterized as EXPTIME-complete as the proof also requires an exponential time to check. Due to the same reason, it cannot be in NP. Chess comes under NP Hard problem.

How hard is NP-hard?

NP-Hard: These are at least as hard as the hardest problems in NP. If we can solve these problems in polynomial time, we can solve any NP problem that can possibly exist. Note that these problems are not necessarily NP problems. That means, we may/may-not verify the solution to these problems in polynomial time.

How do you show NP-hard?

By definition P is contained in NP. If P NP, then any problem that is in P (also in NP) can’t be NP-hard. So the whole class P will be a positive candidate for this question. If P=NP, then all NP problems will be NP-hard under polynomial time reductions.

Why is TSP NP-hard?

Why TSP Is Not NP-complete Since it’s not in NP, it can’t be NP-complete. In TSP you’re looking for the shortest loop that goes through every city in a given set of cities. Since it takes exponential time to solve NP, the solution cannot be checked in polynomial time. Thus this problem is NP-hard, but not in NP.

What makes NP-hard difficult?

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.

Is NP-hard in NP?

The complexity class of problems of this form is called NP, an abbreviation for “nondeterministic polynomial time”. A problem is said to be NP-hard if everything in NP can be transformed in polynomial time into it even though it may not be in NP. The NP-complete problems represent the hardest problems in NP.

Is ATM NP-hard?

(a) Show formally that ATM is NP-hard. Solution: Recall that ATM is RE-hard, and recall that the reduction we used to prove it did the following: for a language L ∈ RE, let M be a TM such that L(M) = L, then given input x, the reduction outputs 〈M,x〉.