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...
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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...
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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...
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computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational problem...
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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...
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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...
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S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York:...
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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...
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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....
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versus NP problem, which is still widely considered the most important unsolved problem in theoretical computer science. The concept of NP-completeness was...
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Computers and Intractability (redirect from Computers and Intractability: A Guide to the Theory of NP-completeness)
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...
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Polynomial-time reduction (section Completeness)
is GI-complete, as are several other related problems. Karp's 21 NP-complete problems MIT OpenCourseWare: 16. Complexity: P, NP, NP-completeness, Reductions...
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Addison-Wesley. ISBN 0-201-44124-1. Chap. 11. Goldreich, Oded (2010). P, NP, and NP-completeness: The Basics of Computational Complexity. Cambridge University Press...
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Hamiltonian path problem (category NP-complete problems)
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...
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complexity class NP-equivalent is the set of function problems that are both NP-easy and NP-hard. NP-equivalent is the analogue of NP-complete for function...
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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...
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S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York:...
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Maximum cut (category NP-complete problems)
be NP-complete. It is easy to see that the problem is in NP: a yes answer is easy to prove by presenting a large enough cut. The NP-completeness of the...
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Not-all-equal 3-satisfiability (category NP-complete problems)
3-satisfiability (NAE3SAT) is an NP-complete variant of the Boolean satisfiability problem, often used in proofs of NP-completeness. Like 3-satisfiability, an...
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would be NP-complete. In 1982, Steve Mahaney published his proof that the nonexistence of sparse NP-complete languages (with NP-completeness defined in...
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Boolean satisfiability problem (category NP-complete problems)
S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman. pp. A9.1: LO1–LO7, pp. 259–260. ISBN 0-7167-1045-5...
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Engineering (1992) for major contributions to the theory and application of NP-completeness, constructing efficient combinatorial algorithms, and applying probabilistic...
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reductions from one computational problem to another, as part of proofs of NP-completeness or other types of computational hardness. The component design technique...
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Graph isomorphism problem (redirect from GI-complete)
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...
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Circuit satisfiability problem (category NP-complete problems)
can be reduced to the other satisfiability problems to prove their NP-completeness. The satisfiability of a circuit containing m {\displaystyle m} arbitrary...
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{\displaystyle O\left(|V|/{\sqrt {\log |V|}}\right)} approximation ratio. The NP-completeness of the achromatic number problem holds also for some special classes...
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Clique problem (category NP-complete problems)
Cook (1971) and Karp (1972), researchers began using the theory of NP-completeness and related intractability results to provide a mathematical explanation...
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Feedback vertex set (category NP-complete problems)
reduction also implies the NP-completeness of the feedback vertex set problem on undirected graphs, where the problem stays NP-complete on graphs of maximum...
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Planar SAT (category NP-complete problems)
of the formula. This problem is NP-complete. Reduction from Planar SAT is a commonly used method in NP-completeness proofs of logic puzzles. Examples...
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theorem. Special cases of Schaefer's dichotomy theorem include the NP-completeness of SAT (the Boolean satisfiability problem) and its two popular variants...
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