3-Hitting set on bounded degree hypergraphs: upper and lower bounds on the kernel size

  • Authors:

  • Iyad A. Kanj;Fenghui Zhang

  • Affiliations:

  • School of Computing, DePaul University, Chicago, IL;Google Kirkland, Kirkland, WA

  • Venue:
  • TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
  • Year:
  • 2011

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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.