KandidatProblem

KandidatProblem is a term used in theoretical computer science and discrete mathematics to describe a class of computational problems that are particularly difficult to solve. These problems are characterized by the fact that finding an exact solution is computationally expensive, often requiring an exponential amount of time with respect to the input size. While a brute-force approach of checking every possible solution is always possible, this becomes infeasible for larger instances of the problem.

The set of KandidatProblems is closely related to the complexity class NP-hard. A problem is considered NP-hard if every problem in the complexity class NP (nondeterministic polynomial time) can be reduced to it in polynomial time. This means that if an efficient (polynomial-time) algorithm were found for any NP-hard problem, then all problems in NP could also be solved efficiently.

Prominent examples of KandidatProblems include the traveling salesman problem, the boolean satisfiability problem (SAT), and the subset sum problem. These problems have a wide range of applications in various fields, including logistics, artificial intelligence, cryptography, and operations research. The ongoing research in this area focuses on developing approximation algorithms that can find near-optimal solutions in a reasonable amount of time, or on identifying specific subclasses of these problems that can be solved more efficiently. The question of whether P equals NP (i.e., if all problems solvable in polynomial time by a nondeterministic Turing machine can also be solved in polynomial time by a deterministic Turing machine) remains one of the most important unsolved problems in computer science, and its resolution would have profound implications for our understanding of computational difficulty.