The Effect of Homogeneity on the Complexity of k-Anonymity

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.