3-hitting set on Bounded Degree Hypergraphs: Upper and Lower Bounds on the Kernel Size

  • Iyad A. Kanj
  • Fenghui Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6595)

Abstract

We study upper and lower bounds on the kernel size for the 3-hitting set problem on hypergraphs of degree at most 3, denoted 3-3-hs. We first show that, unless P=NP, 3-3-hs on 3-uniform hypergraphs does not have a kernel of size at most 35k/19 > 1.8421k. We then give a 4k − k0.2692 kernel for 3-3-hs that is computable in time O(k1.2692). This result improves the upper bound of 4k on the kernel size for 3-3-hs, given by Wahlström. We also show that the upper bound results on the kernel size for 3-3-hs can be generalized to the 3-hs problem on hypergraphs of bounded degree Δ, for any integer-constant Δ> 3.

Keywords

hitting set kernel upper bounds lower bounds parameterized complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Iyad A. Kanj
    • 1
  • Fenghui Zhang
    • 2
  1. 1.School of ComputingDePaul UniversityChicagoUSA
  2. 2.Google KirklandKirklandUSA

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