problems in NP in polynomial time. The concept of NP-completeness was introduced in 1971 (see Cook–Levin theorem), though the term NP-complete was introduced...

NP-complete. An important variant is where each clause has exactly three literals (3SAT), since it is used in the proof of many other NP-completeness...

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

In 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...

To attack the P = NP question, the concept of NP-completeness is very useful. NP-complete problems are problems that any other NP problem is reducible...

computationally intractable, and it drove interest in the study of NP-completeness and the P versus NP problem. Karp's 21 problems are shown below, many with their...

as hard as NP, but not necessarily in NP. NP-equivalent Decision problems that are both NP-hard and NP-easy, but not necessarily in NP. NP-intermediate...

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 as a...

in theoretical computer science as of 2024[update]. The concept of NP-completeness was developed in the late 1960s and early 1970s in parallel by researchers...

Publishing. ISBN 0-534-94728-X. Sections 7.3–7.5 (The Class NP, NP-completeness, Additional NP-complete Problems), pp. 241–271. David Harel, Yishai Feldman....

Theory of NP-Completeness is a textbook by Michael Garey and David S. Johnson. It was the first book exclusively on the theory of NP-completeness and computational...

(2010). P, NP, and NP-completeness: The Basics of Computational Complexity. Cambridge University Press. p. 155. ISBN 9781139490092. Complexity Zoo: coNP...

3-satisfiability (NAE3SAT) is an NP-complete variant of the Boolean satisfiability problem, often used in proofs of NP-completeness. Like 3-satisfiability, an...

S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York:...

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...

NP-completeness, and proved the existence of an NP-complete problem by showing that the Boolean satisfiability problem (usually known as SAT) is NP-complete...

reductions from one computational problem to another, as part of proofs of NP-completeness or other types of computational hardness. The component design technique...

independently discovered the existence of NP-complete problems. This NP-completeness theorem, often called the Cook–Levin theorem, was a basis for one of...

is GI-complete, as are several other related problems. Karp's 21 NP-complete problems MIT OpenCourseWare: 16. Complexity: P, NP, NP-completeness, Reductions...

Look up np in Wiktionary, the free dictionary. NP may refer to: NP (novel), by Japanese author Banana Yoshimoto Nashua-Plainfield Community School District...

problem, finding a solution to a given Numberlink puzzle is NP-complete. NP-completeness is maintained even if "zig-zag" paths are allowed. Informally...

can be reduced to the other satisfiability problems to prove their NP-completeness. The satisfiability of a circuit containing m {\displaystyle m} arbitrary...

a reduction from 3-dimensional matching via 4-partition. To prove NP-completeness of the numerical 3-dimensional matching, the proof should be similar...

position of the problem in the class NP as well as in other complexity classes.) Johnson, David S. (2005), "The NP-Completeness Column", ACM Transactions on Algorithms...

to be NP-complete, by a reduction from 3-dimensional matching. The classic reference by Garey and Johnson (1979) describes an NP-completeness proof,...

Cook (1971) and Karp (1972), researchers began using the theory of NP-completeness and related intractability results to provide a mathematical explanation...

{\displaystyle O\left(|V|/{\sqrt {\log |V|}}\right)} approximation ratio. The NP-completeness of the achromatic number problem holds also for some special classes...

Engineering (1992) for major contributions to the theory and application of NP-completeness, constructing efficient combinatorial algorithms, and applying probabilistic...

be NP-complete. This was proven by Friedman (2002) by constructing puzzles equivalent to arbitrary Boolean circuits, which shows NP-completeness because...

to a 2022 paper by Eammon Hart and Joshua A. McGinnis, Flow Free is NP-complete, meaning computers cannot solve the puzzles in polynomial time as complexity...