### On Parameterized Exponential Time Complexity [chapter]

Jianer Chen, Iyad A. Kanj, Ge Xia
<span title="">2009</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper we study the notion of parameterized exponential time complexity. We show that a parameterized problem can be solved in parameterized 2 o(f (k)) p(n) time if and only if it is solvable in time O(2 δf (k) q(n)) for any constant δ > 0, where p and q are polynomials. We then illustrate how this equivalence can be used to show that special instances of parameterized NP-hard problems are as difficult as the general instances. For example, we show that the Planar Dominating Set problem
more &raquo; ... n degree-3 graphs can be solved in 2 o( √ k) p(n) parameterized time if and only if the general Planar Dominating Set problem can. Apart from their complexity theoretic implications, our results have some interesting algorithmic implications as well.
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