The complexity of minimum difference cover

  • Authors:

  • Carlo Mereghetti;Beatrice Palano

  • Affiliations:

  • Dipartimento di Scienze dell'Informazione, Universití degli Studi di Milano, via Comelico 39, 20135 Milano, Italy;Dipartimento di Scienze dell'Informazione, Universití degli Studi di Milano, via Comelico 39, 20135 Milano, Italy

  • Venue:
  • Journal of Discrete Algorithms
  • Year:
  • 2006

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Abstract

The complexity of searching minimum difference covers, both in Z^+ and in Z"n, is studied. We prove that these two optimization problems are NP-hard. To obtain this result, we characterize those sets-called extrema-having themselves plus zero as minimum difference cover. Such a combinatorial characterization enables us to show that testing whether sets are not extrema, both in Z^+ and in Z"n, is NP-complete. However, for these two decision problems we exhibit pseudo-polynomial time algorithms.