The Effect of Homogeneity on the Complexity of k-Anonymity

  • Robert Bredereck
  • André Nichterlein
  • Rolf Niedermeier
  • Geevarghese Philip
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6914)

Abstract

The NP-hard k-Anonymity problem asks, given an n ×m-matrix M over a fixed alphabet and an integer s > 0, whether M can be made k-anonymous by suppressing (blanking out) at most s entries. A matrix M is said to be k-anonymous if for each row r in M there are at least k–1 other rows in M which are identical to r. Complementing previous work, we introduce two new “data-driven” parameterizations for k-Anonymity—the number \({t_{\textrm{in}}}\) of different input rows and the number \(t_{\textrm{out}}\) of different output rows—both modeling aspects of data homogeneity. We show that k-Anonymity is fixed-parameter tractable for the parameter \({t_{\textrm{in}}}\), and it is NP-hard even for \({t_{\textrm{out}}} = 2\) and alphabet size four. Notably, our fixed-parameter tractability result implies that k-Anonymity can be solved in linear time when \({t_{\textrm{in}}}\) is a constant. Our results also extend to some interesting generalizations of k-Anonymity.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Robert Bredereck
    • 1
  • André Nichterlein
    • 1
  • Rolf Niedermeier
    • 1
  • Geevarghese Philip
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.The Institute of Mathematical SciencesChennaiIndia

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