NP-completeness

In complexity theory, an NP-complete problem (i. e. a complete problem for the NP class) is a decision problem checking the following properties:it is possible to check a solution efficiently (in polynomial time); the class of problems checking this property is denoted NP; all problems of the NP class are reduced to it via polynomial reduction; this means that the problem is at least as difficult as all other problems of the NP class.

An NP-difficult problem is a problem that meets the second condition, and thus may be in a larger and thus more difficult problem class than the NP class.

Although any proposed solution to an NP-complete problem can be quickly verified, it cannot be effectively found. This is the case, for example, with the commercial traveller's problem or the backpack problem.

The concept of NP-completeness was introduced in 1971 by Stephen Cook in a paper entitled The complexity of theorem-proving procedures.

The class NP is the set of languages decidable in polynomial time by a non-deterministic Turing machine.

Links
https://www.ics.uci.edu/~eppstein/cgt/hard.html

Complexity results for scheduling problems

Source
wp(fr):Problème_NP-complet