Abstract
This last chapter of the book is concerned with subexponential fixed-parameter tractability, that is, with the class \( \text{SUBEPT} = 2^{o^{\text{eff}}(k)}-\text{FPT} \). Subexponential fixed-parameter tractability is intimately linked with the theory of exact (exponential) algorithms for hard problems, which is concerned with algorithms for NP-hard problems that are better than the trivial exhaustive search algorithms, though still exponential. For example, there has been a long sequence of papers on exact algorithms for the 3-satisfiability problem; the currently best (randomized) algorithm for this problem has a running time of \( 1.324^n \) time for instances with n variables. There are numerous further examples of very nice nontrivial algorithms for hard problems, but a systematic complexity theory is still in its infancy. A question that has turned out to be central for such a theory is whether the 3-satisfiability problem can be solved in time \( 2^{o(n)} \).
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© 2006 Springer-Verlag Berlin Heidelberg
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(2006). Subexponential Fixed-Parameter Tractability. In: Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-29953-X_16
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DOI: https://doi.org/10.1007/3-540-29953-X_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29952-3
Online ISBN: 978-3-540-29953-0
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