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- W2094650442 abstract "We study a refined framework of parameterized complexity theory where the parameter dependence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some family ℱ . For every family ℱ of functions, this yields a notion of ℱ - fixed-parameter tractability . If ℱ is the class of all polynomially bounded functions, then ℱ -fixed-parameter tractability coincides with polynomial time decidability and if ℱ is the class of all computable functions, ℱ -fixed-parameter tractability coincides with the standard notion of fixed-parameter tractability. There are interesting choices of ℱ between these two extremes, for example the class of all singly exponential functions. In this article, we study the general theory of ℱ -fixed-parameter tractability. We introduce a generic notion of reduction and two classes ℱ -W[P] and ℱ -XP , which may be viewed as analogues of NP and EXPTIME, respectively, in the world of ℱ -fixed-parameter tractability." @default.
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- W2094650442 date "2007-09-01" @default.
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- W2094650442 title "Bounded fixed-parameter tractability and reducibility" @default.
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- W2094650442 doi "https://doi.org/10.1016/j.apal.2007.06.001" @default.
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