The effect of homogeneity on the computational complexity of combinatorial data anonymization

  • Authors:

  • Robert Bredereck;André Nichterlein;Rolf Niedermeier;Geevarghese Philip

  • Affiliations:

  • Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Institut für Softwaretechnik und Theoretische Informatik, TU Berlin, Berlin, Germany;Max-Planck-Institut für Informatik, Saarbrücken, Germany

  • Venue:
  • Data Mining and Knowledge Discovery
  • Year:
  • 2014

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Abstract

A matrix M is said to be k-anonymous if for each row r in M there are at least k 驴 1 other rows in M which are identical to r. The NP-hard k-Anonymity problem asks, given an n 脳 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. Complementing previous work, we introduce two new "data-driven" parameterizations for k-Anonymity--the number t in of different input rows and the number t out of different output rows--both modeling aspects of data homogeneity. We show that k-Anonymity is fixed-parameter tractable for the parameter t in , and that it is NP-hard even for t out = 2 and alphabet size four. Notably, our fixed-parameter tractability result implies that k-Anonymity can be solved in linear time when t in is a constant. Our computational hardness results also extend to the related privacy problems p-Sensitivity and ℓ-Diversity, while our fixed-parameter tractability results extend to p-Sensitivity and the usage of domain generalization hierarchies, where the entries are replaced by more general data instead of being completely suppressed.