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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.

Keywords

Parameterized Complexity Output Type Alphabet Size Combine Parameter Partition Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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