parameterisierte

Parameterisierte is the adjective form used to describe something expressed or defined in terms of one or more parameters. In mathematics and geometry, parameterization is the practice of describing a geometric object by a function of parameters. For a curve, a parameterization assigns a point on the curve to each value of a parameter t, via equations such as x = f(t) and y = g(t). As t varies, the resulting points trace the object. Surfaces and higher-dimensional shapes can be parameterized by two or more parameters.

Beyond pure geometry, parameterized ideas appear in statistics, machine learning, and computer science. A parametric model describes a family of distributions or functions using a finite set of parameters. In optimization and numerical methods, parameterized problems include data together with parameters that influence the objective or constraints.

In computer science, parameterized complexity analyzes problems with respect to a parameter k in addition to input size n. This framework leads to concepts such as fixed-parameter tractability, where running times have the form f(k)·n^O(1), making some hard problems tractable for small k. Kernelization and other reduction techniques are also central to this approach, reducing instances to a size depending only on k.

Examples include the Vertex Cover problem, which is NP-hard in general but admits fixed-parameter tractable algorithms with respect to the solution size k. The term parameterisierte is commonly used in German-language contexts to denote such parameter-dependent descriptions, models, or algorithms, and parallels the English term parameterized across various fields.