On parameterized exponential time complexity

Jianer Chen, Iyad A. Kanj, Ge Xia
2009 Theoretical Computer Science  
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 » ... 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.
doi:10.1016/j.tcs.2009.03.006 fatcat:i2qixnqsvjaoveyv7b2wmotsnq