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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 problemdoi:10.1016/j.tcs.2009.03.006 fatcat:i2qixnqsvjaoveyv7b2wmotsnq