The Effect of Homogeneity on the Complexity of k-Anonymity

摘要

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" parameter-izations 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 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 results also extend to some interesting generalizations of k-Anonymity.