The complexity of the matroid–greedoid partition problem

  • Authors:
  • Vera Asodi;Christopher Umans

  • Affiliations:
  • California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, United States;California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, United States

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

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Abstract

We show that the maximum matroid-greedoid partition problem isNP-hard to approximate to within 1/2+ε for anyε0, which matches the trivial factor 1/2 approximationalgorithm. The main tool in our hardness of approximation result isan extractor code with polynomial rate, alphabet size andlist size, together with an efficient algorithm for list-decoding.We show that the recent extractor construction of Guruswami, Umansand Vadhan [V. Guruswami, C. Umans, S.P. Vadhan, Unbalancedexpanders and randomness extractors from Parvaresh-Vardy codes, in:IEEE Conference on Computational Complexity, IEEE Computer Society,2007, pp. 96-108] can be used to obtain a code with theseproperties. We also show that the parameterized matroid-greedoidpartition problem is fixed-parameter tractable.