NPtäydellisyys

NPtäydellisyys is a Finnish term that translates to "NP-completeness" in English. It refers to a class of computational problems for which no known efficient algorithm exists to find a solution. These problems are characterized by the fact that if a solution can be found for one NP-complete problem in polynomial time, then all problems in the NP class can be solved in polynomial time.

The class NP stands for Nondeterministic Polynomial time. A problem is in NP if, given a potential solution, it is possible to verify its correctness in polynomial time. NP-complete problems are the "hardest" problems in NP, meaning they are at least as difficult as any other problem in NP.

Examples of NP-complete problems include the Traveling Salesperson Problem, the Boolean satisfiability problem (SAT), and the knapsack problem. These problems have significant implications in various fields, including computer science, operations research, and artificial intelligence. While no efficient algorithm is known for solving NP-complete problems in general, heuristics and approximation algorithms are often used to find good, though not necessarily optimal, solutions. The P versus NP problem, which asks whether every problem whose solution can be quickly verified can also be quickly solved, remains one of the most important unsolved problems in theoretical computer science.