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This diagram uses embedded text that can be easily translated using a text editor. Valued image This image has been assessed under the valued image criteria and is considered the most valued image on Commons within the scope: P versus NP problem .
Euler diagram for P, NP, NP-complete, and NP-hard set of problems (excluding the empty language and its complement, which belong to P but are not NP-complete) Main article: NP-completeness To attack the P = NP question, the concept of NP-completeness is very useful.
Euler diagram for P, NP, NP-complete, and NP-hard set of problems. Under the assumption that P ≠ NP, the existence of problems within NP but outside both P and NP-complete was established by Ladner. [1] In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.
The answer is not known, but it is believed that the problem is at least not NP-complete. [8] If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level. [9] Since it is widely believed that the polynomial hierarchy does not collapse to any finite level, it is believed that graph isomorphism is not NP-complete.
The MAX-SAT problem is OptP-complete, [1] and thus NP-hard (as a decision problem), since its solution easily leads to the solution of the boolean satisfiability problem, which is NP-complete. It is also difficult to find an approximate solution of the problem, that satisfies a number of clauses within a guaranteed approximation ratio of the ...
Euler diagram for P, NP, NP-complete, and NP-hard sets of problems. The left side is valid under the assumption that P≠NP , while the right side is valid under the assumption that P=NP (except that the empty language and its complement are never NP-complete, and in general, not every problem in P or NP is NP-complete).
The Hamiltonian path problem and the Hamiltonian cycle problem belong to the class of NP-complete problems, as shown in Michael Garey and David S. Johnson's book Computers and Intractability: A Guide to the Theory of NP-Completeness and Richard Karp's list of 21 NP-complete problems. [2] [3]
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...