On parameterized exponential time complexity

  • Authors:

  • Jianer Chen;Iyad A. Kanj;Ge Xia

  • Affiliations:

  • Department of Computer Science and Engineering, Texas A&M University, College Station, TX 77843, United States;School of Computing, DePaul University, 243 S. Wabash Avenue, Chicago, IL 60604, United States;Department of Computer Science, Lafayette College, Easton, PA 18042, United States

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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Abstract

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^@d^f^(^k^)q(n)) for any constant @d0, 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 on 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.