computer science The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution...

theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete...

solve than all problems in NP, but they are probably not NP-hard (unless P=NP). A decision problem H is NP-hard when for every problem L in NP, there is a...

Unsolved problem in computer science P   = ?   N P {\displaystyle {\mathsf {P\ {\overset {?}{=}}\ NP}}} More unsolved problems in computer science In...

the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known, this list is in...

21 NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility Among Combinatorial Problems", Richard...

graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization problem. It is NP-hard, so it cannot be solved by...

the first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes...

theory, co-NP is a complexity class. A decision problem X is a member of co-NP if and only if its complement X is in the complexity class NP. The class...

scheduling problems. The NP-hardness of the unweighted longest path problem can be shown using a reduction from the Hamiltonian path problem: a graph G...

asked whether a certain NP-complete problem could be solved in quadratic or linear time. The precise statement of the P=NP problem was introduced in 1971...

precisely T {\displaystyle T} . The problem is known to be NP-complete. Moreover, some restricted variants of it are NP-complete too, for example: The variant...

Hamiltonian cycle. The Hamiltonian path problem and the Hamiltonian cycle problem belong to the class of NP-complete problems, as shown in Michael Garey and David...

is NP-hard, but can be solved efficiently in practice. The partition problem is a special case of two related problems: In the subset sum problem, the...

conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Riemann hypothesis, Yang–Mills existence and mass gap, and the Poincaré...

complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational problem may have numerical...

problem is solvable in polynomial time, GI would equal P. On the other hand, if the problem is NP-complete, GI would equal NP and all problems in NP would...

#P (pronounced "sharp P" or, sometimes "number P" or "hash P") is the set of the counting problems associated with the decision problems in the set NP...

are used. #P-complete problems are at least as hard as NP-complete problems. A polynomial-time algorithm for solving a #P-complete problem, if it existed...

covering is NP-complete. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. The optimization/search version of set cover is NP-hard...

Euclidean Steiner tree problem is NP-complete, since membership to the complexity class NP is not known. The rectilinear Steiner tree problem is a variant of...

makes the problem NP-complete (such problems are not believed to be efficiently solvable for large sets of data, see P = NP problem). Another NP-complete...

problem are hard. The clique decision problem is NP-complete (one of Karp's 21 NP-complete problems). The problem of finding the maximum clique is both...

both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain...

states that the Boolean satisfiability problem is NP-complete. That is, it is in NP, and any problem in NP can be reduced in polynomial time by a deterministic...

discrete optimization problems are NP-complete, such as the traveling salesman (decision) problem, this is expected unless P=NP. For each combinatorial...

computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated...

computational complexity, problems that are in the complexity class NP but are neither in the class P nor NP-complete are called NP-intermediate, and the...

class NP-complete, a class of decision problems NP-hard, a class of problems in computational complexity Co-NP, a complexity class Numpy a Python mathematical...

answer questions about the fundamental nature of computation. The P versus NP problem, for instance, is directly related to questions of whether nondeterminism...