Definition
Parameterized complexity theory is the study of the interaction between the fixing of parameters of input problems and their computational complexity. A central parameterized complexity concept is that of a fixed-parameter tractable (FPT) problem, which captures a strong notion of well-behavedness of a problem under the assumption that parameter values do not grow with input sizes. There is also a solid theory of fixed-parameter intractability, which gives strong evidence that for certain parameterizations of problems, no FPT algorithms can be found.
Historical Background
Fixed-parameter complexity theory is strongly associated with R. Downey and M. Fellows, who did much seminal work in the area (cf. [3, 5]). The first fixed-parameter complexity result in the context of database query evaluation was the linear-time query processing algorithm for acyclic conjunctive queries by Yannakakis in 1981 [12], which preceded the development of parameterized complexity theory (cf....
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Koch, C. (2018). Parameterized Complexity of Queries. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_1244
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