Abstract 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 NPhard 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.
For example, the problem becomes fixed-parameter tractable for the parameter "number of different input rows" or for the parameter combination "number of different output row types" and "number of suppressions" REF .
The effect of homogeneity on the computational complexity of combinatorial data anonymization
Data Mining and Knowledge Discovery
Data Mining and Knowledge Discovery
Mathematics Computer Science