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...
30 KB (3,617 words) - 17:49, 12 November 2024
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...
29 KB (2,746 words) - 10:59, 2 November 2024
computational complexity, strong NP-completeness is a property of computational problems that is a special case of NP-completeness. A general computational problem...
4 KB (642 words) - 19:47, 7 May 2023
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...
2 KB (429 words) - 23:56, 28 May 2022
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...
63 KB (7,782 words) - 18:22, 10 November 2024
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...
5 KB (486 words) - 13:35, 25 April 2023
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...
3 KB (369 words) - 23:34, 6 May 2021
S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York:...
8 KB (1,082 words) - 12:35, 14 October 2024
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....
21 KB (2,787 words) - 14:08, 19 September 2024
versus NP problem, which is still widely considered the most important unsolved problem in theoretical computer science. The concept of NP-completeness was...
19 KB (2,355 words) - 22:12, 5 November 2024
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...
7 KB (779 words) - 07:12, 8 May 2023
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...
7 KB (948 words) - 22:59, 23 November 2024
Look up np in Wiktionary, the free dictionary. NP may refer to: NP (novel), by Japanese author Banana Yoshimoto Nashua-Plainfield Community School District...
2 KB (285 words) - 20:59, 17 November 2024
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...
5 KB (641 words) - 19:16, 11 October 2023
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...
11 KB (1,472 words) - 23:39, 6 June 2023
{\displaystyle O\left(|V|/{\sqrt {\log |V|}}\right)} approximation ratio. The NP-completeness of the achromatic number problem holds also for some special classes...
6 KB (614 words) - 10:20, 13 October 2024
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...
3 KB (450 words) - 11:55, 11 January 2023
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...
40 KB (4,127 words) - 14:57, 25 October 2024
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...
16 KB (1,510 words) - 19:27, 11 November 2024
independently discovered the existence of NP-complete problems. This NP-completeness theorem, often called the Cook–Levin theorem, was a basis for one of...
8 KB (656 words) - 08:51, 25 October 2024
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...
21 KB (2,518 words) - 19:02, 20 August 2024
S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York:...
49 KB (6,717 words) - 21:56, 25 September 2024
reductions from one computational problem to another, as part of proofs of NP-completeness or other types of computational hardness. The component design technique...
13 KB (1,604 words) - 03:05, 18 March 2024
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...
9 KB (1,183 words) - 06:50, 30 April 2024
S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences (1st ed.). New York:...
2 KB (290 words) - 20:58, 8 May 2024
Numerical 3-dimensional matching (category Strongly NP-complete problems)
a reduction from 3-dimensional matching via 4-partition. To prove NP-completeness of the numerical 3-dimensional matching, the proof should be similar...
4 KB (689 words) - 00:40, 23 April 2024
Feedback vertex set (category NP-complete problems)
Karp's reduction also implies the NP-completeness of the FVS problem on undirected graphs, where the problem stays NP-hard on graphs of maximum degree...
16 KB (1,781 words) - 21:22, 20 August 2024
Boolean satisfiability problem (category NP-complete problems)
is listed as NP-complete problem "LO4" in the standard reference Computers and Intractability: A Guide to the Theory of NP-Completeness by Michael R....
52 KB (5,326 words) - 08:55, 3 November 2024
Minesweeper (video game) (category NP-complete problems)
original (PDF) on 9 June 2019. — An open-access paper explaining Kaye's NP-completeness result. Richard Kaye's Minesweeper pages Microsoft Minesweeper playable...
20 KB (2,027 words) - 05:21, 23 October 2024
Pseudo-polynomial time (section Strong and weak NP-hardness vs. strong and weak polynomial-time algorithms)
S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, 1979. Demaine, Erik. "Algorithmic Lower...
5 KB (876 words) - 07:57, 4 December 2023