The sharing of databases either within or across organizations raises the possibility of unintentionally revealing sensitive relationships contained in them. Recent advances in data-mining technology have increased the chances of such disclosure. Consequently, firms that share their databases might choose to hide these sensitive relationships prior to sharing. Ideally, the approach used to hide relationships should be impervious to as many data-mining techniques as possible, while minimizing the resulting distortion to the database. This paper focuses on frequent item sets, the identification of which forms a critical initial step in a variety of data-mining tasks. It presents an optimal approach for hiding sensitive item sets, while keeping the number of modified transactions to a minimum. The approach is particularly attractive as it easily handles databases with millions of transactions. Results from extensive tests conducted on publicly available real data and data generated using IBM's synthetic data generator indicate that the approach presented is very effective, optimally solving problems involving millions of transactions in a few seconds.