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.

What are examples of NP-complete problems?

NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.

Is sorting a list NP-complete?

Sorting Numbers Given a list of numbers, you can verify that whether the list is sorted or not 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. ).

How do you show that a problem is NP-complete?

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 a new problem is NP-complete by reducing some other NP-complete problem to it.

Is N Queens NP-complete?

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

What is an NP complete?

(definition) Definition: The complexity class of decision problems for which answers can be checked for correctness, given a certificate, by an algorithm whose run time is polynomial in the size of the input (that is, it is NP) and no other NP problem is more than a polynomial factor harder.

Is sat NP complete?

Algorithms for solving SAT. Since the SAT problem is NP-complete, only algorithms with exponential worst-case complexity are known for it.

Is 8 queens problem NP-complete?

N Queens Completion Is NP Complete. The problem of putting eight queens on the chess board so as no queen attacks another is a solved problem, as is placing n queens on an nxn board. However if you place some queens on the board and ask for a completion then the problem is NP complete.

Can NP-complete problems be solved in polynomial time?

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.

What do you call problems that are NP complete?

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. The phenomenon of NP-completeness is important for both theoretical and practical reasons.

What are some examples of NP hard classes?

NP Hard and NP-Complete Classes 1 Definition of NP-Completeness. Every A in NP is polynomial time reducible to B. 2 NP-Complete Problems. Following are some NP-Complete problems, for which no polynomial time algorithm is known. 3 NP-Hard Problems. The traveling salesman problem consists of a salesman and a set of cities. 4 Proof.

Is the set cover problem a NP complete problem?

Set cover (also called minimum cover problem) This is equivalent, by transposing the incidence matrix, to the hitting set problem. Variations on the Traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers.

When is a search problem a NP hard?

Informally, a search problem B is NP-Hard if there exists some NP-Complete problem A that Turing reduces to B. The problem in NP-Hard cannot be solved in polynomial time, until P = NP. If a problem is proved to be NPC, there is no need to waste time on trying to find an efficient algorithm for it.