aproksimaatiosuunnitelma

Aproksimaatiosuunnitelma, often translated as approximation plan or approximation algorithm, is a concept in computer science, particularly in the field of algorithm design and analysis. It refers to a strategy for solving optimization problems for which finding an exact optimal solution is computationally very difficult or impossible within a reasonable amount of time. These problems are often classified as NP-hard.

Instead of seeking the absolute best solution, an aproksimaatiosuunnitelma aims to find a solution that is provably close to the optimal one. The "closeness" is typically defined by an approximation ratio. For a minimization problem, an approximation algorithm guarantees that the solution it finds is at most a constant factor (the approximation ratio) times the value of the true optimal solution. For a maximization problem, the found solution is at least a constant factor times the optimal value.

The development of aproksimaatiosuunnitelmia is crucial for tackling real-world problems where obtaining an exact solution is infeasible. Examples include problems in routing, scheduling, and resource allocation. The performance of an approximation algorithm is evaluated not only by its approximation ratio but also by its running time. Ideally, an approximation algorithm should run in polynomial time, making it efficient even for large problem instances. Research in this area focuses on designing algorithms with the best possible approximation ratios and the fastest running times.