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...

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...

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

NP-complete problem with known pseudo-polynomial time algorithms is called weakly NP-complete. An NP-complete problem is called strongly NP-complete if...

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

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...

ISSN 1572-5286. S2CID 8820628. Wojtczak, Dominik (2018). "On Strong NP-Completeness of Rational Problems". Computer Science – Theory and Applications....

Intractability; A Guide to the Theory of NP-Completeness. pp. 96–105. ISBN 978-0-7167-1045-5. Goodrich, Michael. "More NP complete and NP hard problems" (PDF). Hans...

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...

Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is soundness, the fact that only logically...

problem is NP-hard and the decision version of the problem, which asks whether a path exists of at least some given length, is NP-complete. This means...

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

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

reduction that can be used to prove the NP-completeness of the clique cover problem from the known NP-completeness of graph coloring. Perfect graphs are...

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

average-case complexity and completeness while giving an example of a complete problem for distNP, the average-case analogue of NP. The first task is to precisely...

cases. Usually for P-completeness, NC-reduction is meant by default, though many results in the literature concerning P-completeness still holds even under...

obtaining PPAD-completeness is a weaker evidence of intractability than that of obtaining NP-completeness. PPAD problems cannot be NP-complete, for the technical...

outerplanar graphs may be solved in linear time, in contrast to the NP-completeness of these problems for arbitrary graphs. Every maximal outerplanar graph...

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

special sense of completeness, in which the class of models (up to isomorphism) is restricted to the intended one. The original completeness proof applies...

3: ND22–24". Computers and Intractability: A Guide to the Theory of NP-completeness. W. H. Freeman. pp. 211–212. ISBN 978-0-7167-1044-8. Goldberg, D. E...

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...

only. (This follows from Kolmogorov's zero–one law.) This is only weak evidence that P≠NP, since a statement may be true for a random oracle but false for...

condition is strictly weaker than functional completeness. Emil Post proved that a set of logical connectives is functionally complete if and only if it is...

it is correct. All interactive proof systems have two requirements: Completeness: if the statement is true, the honest prover (that is, one following...

experts in the field disagree about proposed solutions. P versus NP problem – The P vs NP problem is a major unsolved question in computer science that asks...

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...

programming. Deciding whether a given clause θ-subsumes another is an NP-complete problem. A clause, that is, a disjunction of first-order literals, can...

unsolved P versus NP problem asks if all problems in NP have polynomial-time algorithms. All the best-known algorithms for NP-complete problems like 3SAT...