On Parameterized Exponential Time Complexity

  • Authors:

  • Jianer Chen;Iyad A. Kanj;Ge Xia

  • Affiliations:

  • Department of Computer Science and Engineering, Texas A&M University, USA TX 77843;School of CTI, DePaul University, Chicago, USA IL 60604;Department of Computer Science, Lafayette College, Easton, USA PA 18042

  • Venue:
  • TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
  • Year:
  • 2009

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Abstract

In this paper, we show that special instances of parameterized NP-hard problems are as difficult as the general instances in terms of their subexponential time computability. For example, we show that the Planar Dominating Set problem on degree-3 graphs can be solved in $2^{o(\sqrt{k})} p(n)$ 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.