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

computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes"...

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...

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...

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...

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...

computational complexity, an NP-complete (or NP-hard) problem is weakly NP-complete (or weakly NP-hard) if there is an algorithm for the problem whose running time...

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...

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...

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...

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...

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...

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...

and P ≠ NP, then for many important problems it is not only impossible to get an exact solution in polynomial time (as postulated by the P versus NP problem)...

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...

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...

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...

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...

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...

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...

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...

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

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...

possible). Just as NP has NP-complete problems via many-one reductions, #P has #P-complete problems via parsimonious reductions, problem transformations...

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