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

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...

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...

allows to derive strong NP-completeness from existence of a transformation: If Π 1 {\displaystyle \Pi _{1}} is a strongly NP-complete decision problem...

The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned...

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...

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

 29, ISBN 9780199233212. Garey, M. R.; Johnson, D. S. (1978), "'Strong' NP-completeness results: Motivation, examples, and implications", Journal of the...

{\displaystyle j} . The bin packing problem is strongly NP-complete. This can be proven by reducing the strongly NP-complete 3-partition problem to bin packing....

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

Gödel's completeness theorem establishes semantic completeness for first-order logic. A formal system S is strongly complete or complete in the strong sense...

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

Royle (2001), p. 3. Garey, M. R.; Johnson, D. S. (1978-07-01). ""Strong" NP-Completeness Results: Motivation, Examples, and Implications". Journal of the...

JSTOR 2289017, MR 0860518. Garey, M. R.; Johnson, D. S. (1978), ""Strong" NP-completeness results: motivation, examples and implications", Journal of the...

cannot be solved in polynomial time for arbitrary graphs unless P = NP. Stronger hardness results are also known showing that it is difficult to approximate...

(other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0–1 integer linear programming, in...

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

Retrieved October 3, 2011. Manyem, Prabhu (2010). "Duality Gap, Computational Complexity and NP Completeness: A Survey". arXiv:1012.5568 [math.OC]....

minimize the wasted material. This problem was first studied in 1980. It is strongly-NP hard and there exists no polynomial-time approximation algorithm with...

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

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...

"Section 7.4: Polynomial Space Completeness", Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman, pp. 170–177, ISBN 0-7167-1045-5...

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...

satisfying all demands is NP-complete, even for only two commodities and unit capacities (making the problem strongly NP-complete in this case). If fractional...

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...

brute-force attacks. The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous...

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

{\displaystyle f(n)} -APX-complete classes; some such classes contain well-known optimization problems. Log-APX-completeness and poly-APX-completeness are defined in...

algorithms. It was one of Richard M. Karp's original set of 21 NP-complete problems; its NP-completeness was proved by Karp and Eugene Lawler by showing that inputs...

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...