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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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

#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...

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 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...

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...

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

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...

Boolean satisfiability problem (SAT), and likewise, has been proven to be NP-complete. It is a prototypical NP-complete problem; the Cook–Levin theorem...

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...

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

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