, Volume 28, Issue 1, pp 65-91
Date: 13 Oct 2012

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

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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. 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. 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 -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.

Responsible editor: Jian Pei.
An extended abstract entitled “The Effect of Homogeneity on the Complexity of k-Anonymity” appeared in Proceedings of the 18th International Symposium on Fundamentals of Computation Theory (FCT ’11), volume 6914 of LNCS, pages 53-64, Springer 2011. Apart from the full proofs omitted in that version, the current article also contains new results on ℓ-Diversity, p-Sensitivity, and on the usage of domain generalization hierarchies.