A kernelization algorithm for d-Hitting Set

  • Authors:

  • Faisal N. Abu-Khzam

  • Affiliations:

  • Department of Computer Science and Mathematics, Lebanese American University, 475 Riverside Drive, Suite 1846, New York, NY 10115-0065, USA

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2010

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Abstract

For a given parameterized problem, @p, a kernelization algorithm is a polynomial-time pre-processing procedure that transforms an arbitrary instance of @p into an equivalent one whose size depends only on the input parameter(s). The resulting instance is called a problem kernel. In this paper, a kernelization algorithm for the 3-Hitting Set problem is presented along with a general kernelization for d-Hitting Set. For 3-Hitting Set, an arbitrary instance is reduced into an equivalent one that contains at most 5k^2+k elements. This kernelization is an improvement over previously known methods that guarantee cubic-order kernels. Our method is used also to obtain quadratic kernels for several other problems. For a constant d=3, a kernelization of d-Hitting Set is achieved by a non-trivial generalization of the 3-Hitting Set method, and guarantees a kernel whose order does not exceed (2d-1)k^d^-^1+k.