A three-phase algorithm for the cell suppression problem in two-dimensional statistical tables

To obtain full cooperation from respondents, statistical offices must guarantee that confidential data will not be disclosed when their reports are published. For tabular data, cell suppression is one of the preferred techniques to control statistical disclosure. When suppressing only confidential values does not guarantee the desired data protection, it is also necessary to suppress the values in some non-confidential cells. The problem of finding an optimal set of complementary suppressions—the cell suppression problem (CSP)—is NP-hard. We present a three-phase algorithm for the CSP based on a binary relaxation derived from row and column protection conditions. To enforce violated single cell conditions, integer cuts are added to the CSP relaxation. The numerical results obtained in 1410 instances with up to more than 250?000 cells, which were generated to reproduce two classes of real-world data, indicate that the algorithm is quite effective for both classes of instances and that it outperforms state-of-the-art algorithms for one of them.