NPvollständige

NPvollständige is a German term that translates to NP-complete in English. It refers to a class of computational problems in computer science that are considered the hardest problems in the complexity class NP. NP stands for nondeterministic polynomial time.

Problems in NP are those for which a given solution can be verified in polynomial time by a deterministic algorithm. NP-complete problems have the additional property that any other problem in NP can be reduced to them in polynomial time. This means that if an efficient (polynomial-time) algorithm were found for any NP-complete problem, then all problems in NP could be solved efficiently.

Currently, no polynomial-time algorithm is known for any NP-complete problem. This is a major open question in computer science, known as the P versus NP problem. Most computer scientists believe that P is not equal to NP, meaning that NP-complete problems are inherently harder to solve than problems in P (problems solvable in polynomial time).

Examples of NP-complete problems include the traveling salesman problem, the boolean satisfiability problem (SAT), and the knapsack problem. These problems have significant practical implications in various fields, such as optimization, cryptography, and artificial intelligence. The difficulty of NP-complete problems makes them a focal point of research in theoretical computer science.