Fixed-parameter algorithms provide optimal solutions to given discrete combinatorial problems. As a rule, the problems considered are NP-difficult, so you have to deal with exponential run-time. However, the exponential growth of the runtime may only depend on certain, problem-specific parameters that are part of the input. The goal is to identify such parameters: if the values of these parameters are then small in concrete applications of the particular problem, the exponential growth may be accepted and the problem can be solved efficiently with a fixed-parameter algorithm. Such a parameter can be, for example, the top of a graph: many graph problems are quickly solvable for graphs with a small tree.
Parametrized algorithms provide exact solutions, making them an interesting alternative to heuristics and approximative algorithms.
