Abstract
We introduce the W-hierarchy of parameterized complexity classes in the tower
Presumably, all the inclusions are proper. The W-Hierarchy gives us means of comparing parameterized problems that are presumably not in FPT, with respect to the “strength” of their parameterized intractability. The key idea is to use a form of circuit depth in defining the classes. We discuss the remarkable fact that “almost all” (or at least a very large percentage) of the natural parameterized problems investigated to date are precisely complete for one of the first three classes in this hierarchy, a remarkable empirical finding that supports the definitional framework. We also introduce a natural generalization called the W ∗[t]-hierarchy, about which only a little (but for exact parameterized complexity analysis, a useful little), is so far known.
Keywords
- Natural Parameterized Problems
- Parametric Complexity Class
- Input Output Path
- Normalization Theorem
- Choice Block
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Notes
- 1.
It is also possible to consider families of circuits where small gates may have fan-in f(k), then we can equivalently substitute a faster-growing function h.
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Downey, R.G., Fellows, M.R. (2013). The W-Hierarchy. In: Fundamentals of Parameterized Complexity. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-5559-1_23
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DOI: https://doi.org/10.1007/978-1-4471-5559-1_23
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