NP-complete problem, any one Categories of Computational Problems Computational Problems In theoretical computer science, computational problems are Questions a computer might be able to solve or a question a computer might be able to answer. For example, factoring issues. « Given a positive integer n, find the non-trivial prime factors of n. » https://en.wikipedia.org › wiki › Computational_problem

No valid solution foundMany important computer science problems fall into this category – for example, the traveling salesman problem, the satisfiability problem, and the graph covering problem.

How many NP-complete problems are there?

This list is by no means comprehensive (there are Over 3000 known NP-complete problems). Most of the questions 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 presented here in the same order and organization.

How do you know if a problem is NP-complete?

A sort of decision problem L is NP-complete if: 1) L is in NP (any given solution to an NP-complete problem can be quickly verified, but no efficient known solution). 2) Every problem in NP can be reduced to L in polynomial time (reduction is defined below).

What is NP-completeness, give an example of an NP-complete problem?

NP-Complete problems can be solved in polynomial time by non-deterministic algorithms/Turing machines. To solve this problem, it doesn’t have to be in NP. …it’s all a matter of decision making. example: Stopping problems, vertex cover problems, circuit satisfiability problemsetc.

Is the sorting problem NP-complete?

Sort numbers

Given a list of numbers, you can verify that the list is sorted in polynomial time, so The problem is clearly NP. There are known algorithms to sort a list of numbers in polynomial time. (bubble sort O(n^2) etc.).

8. NP-Hard and NP-Complete problems

18 related questions found

What types of problems might be NP-hard?

if all the problems NP is polynomial time reducible to it, even though it may not be in NP itself. If there is a polynomial-time algorithm for any of these problems, then all problems in NP will be polynomial-time solvable.

Is N Queens NP complete?

The n-queen completion puzzle is a common mathematical problem in computer science and is described as « NP complete« . These are interesting problems because if an efficient solution can be found for an NP-complete problem, it can be used to solve all NP-complete problems.

What is an example of an NP problem?

An example of an NP-hard problem is Decision Subsets and Problems: Given a set of integers, do any non-empty subsets of them add up to zero? This is a decision problem, which happens to be NP-complete.

Can the NP problem be solved?

The short answer is If the problem is in NP, it is indeed solvable.

Can NP-hard problems be solved?

This is called Cook’s theorem. What makes NP-complete problems important is that if a deterministic polynomial time algorithm can be found to solve one of these problems, Every NP problem can be solved in polynomial time (a problem to rule them all).

What does it mean if Q is NP-hard?

A problem is NP-hard if the algorithm that solves the problem can be transformed into an algorithm that solves any NP problem (non-deterministic polynomial time) problem.Therefore, NP-hard means « in as hard as any NP problem« , despite the fact that it may be harder.

Can NP-hard be reduced to NP-complete?

(If P and NP are of the same class, there is no NP-intermediate problem, because in this case every NP-complete problem belongs to P, and by definition, Every problem in NP can be reduced to NP-complete problem. )

Can P be reduced to NP?

Quick Reply: no, no. Recall the definition of an NP-hard problem. A problem X is NP-Hard if every problem in NP is polynomially reducible to X. On the other hand, if a problem X is polynomially reducible to some NP-complete problem Y, it means that Y is at least as hard as X, not the other way around.

How can I prove my 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.In other words, we can prove that a new problem is NP-complete reduce some other NPs– Complete question.

Is NP equal to NP complete?

If both are the same, what’s the point of classifying them? In other words, if we have an NP problem, then by (2) this problem can be transformed into an NP-complete problem.Therefore, the NP problem is now NP-complete, and NP = NP-complete. The two classes are equivalent.

Is it possible that the problem occurs in both P and NP?

Is it possible that the problem occurs in both P and NP? Yes. Because P is a subset of NP, every problem in P is in both P and NP.

What happens if P vs NP is solved?

If P equals NP, Every NP problem contains a hidden shortcut, let the computer quickly find the perfect solution for them. But if P is not equal to NP, there is no such shortcut, and the computer’s ability to solve problems will be fundamentally and permanently limited.

Can P vs NP be solved?

P is the set of all efficiently solvable decision problems is a subset of NP. Basic arithmetic is solvable in polynomial time and therefore belongs to P.

Is NP equal to P?

6 answers. P stands for polynomial time. NP representative nondeterministic polynomial time.

Are Euler cycles NP-complete?

If a graph has an Euler cycle, it is called an Euler graph; if it has an Euler path, it is called a semi-Eulerian graph.The problem seems to be similar to the Hamiltonian path is an NP-complete problem for general graphs. Fortunately, we can find out if a given graph has an Euler path in polynomial time.

Why is the knapsack problem NP-hard?

The time required increases exponentially, so this is an NPC problem.This is because of the knapsack problem has a pseudopolynomial solution Hence it is called weak NP-complete (rather than strong NP-complete).

Is 8 queens a problem in NP?

N Queen completion is NP completion. The problem of placing eight queens on a chessboard so that no queen attacks another queen is a solved problem, just like placing n queens on an nxn chessboard. However, if you put some queens on the board and ask for completion, then the problem is NP-complete.

Are n queens solvable?

n queens problem Solvable for n=1 and n≥4. So the decision problem can be solved in constant time.

What is the 8 queens problem in DAA?

The eight queens problem is The problem of placing eight queens on an 8×8 board so none of them attack each other (No two are on the same row, column, or diagonal). More generally, the n queens problem puts n queens on an n×n chessboard. There are different solutions to this problem.

How are P and NP problems related?

NP is a set of problems Can be solved Via a non-deterministic Turing machine in polynomial time. P is a subset of NP (any problem that can be solved by a deterministic machine in polynomial time can also be solved by a non-deterministic machine in polynomial time) but P≠NP.