On the existence of subexponential parameterized algorithms

  • Authors:
  • Liming Cai;David Juedes

  • Affiliations:
  • Department of Computer Science, University of Georgia, Athens, GA;School of Electrical Engineering and Computer Science, Ohio University, Athens, OH

  • Venue:
  • Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
  • Year:
  • 2003

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Abstract

The existence of subexponential-time parameterized algorithms is examined for various parameterized problems solvable in time O(2o(k)p(n)). It is shown that for each t ≥ 1, there are parameterized problems in FPT for which the existence of O(2o(k)p(n))-time parameterized algorithms implies the collapse of W[t] to FPT. Evidence is demonstrated that Max-SNP-hard optimization problems do not admit subexponential-time parameterized algorithms. In particular, it is shown that each Max-SNP-complete problem is solvable in time O(2o(k)p(n)) if and only if 3-SAT ∈ DTIME(2o(n)). These results are also applied to show evidence for the non-existence of O(2o(√k)p(n))-time parameterized algorithms for a number of other important problems such as Dominating Set, Vertex Cover, and Independent Set on planar graph instances.