A Data Structure and Integer Programming Technique to Facilitate Cell Suppression Strategies

The U.S. Bureau of the Census has the responsibility to collect data regarding economic sectors and to publish these data without violating confidentiality laws. Collected data contain sensitive data values that if directly published could identify an individual establishment's data. There are a number of methods available that prevent compromising the sensitive cells. These disclosure avoidance techniques include rounding, perturbation, and cell suppression, and are outlined in Cox, et al. (1986a).The Bureau's current practice is to protect any cell where n or fewer respondents make up k percent or more of a table cell's value (Zayatz, 1992). (The values of n and k are confidential.) Since rounding and perturbation are unsatisfactory for economic aggregate magnitude data (Cox, et al. 1986b), the Economic Divisions have always chosen a cell suppression technique to protect published tabular data. Instead of the sensitive data value appearing in the publication, a "D" appears in its place. However, in most cases, the sensitive data values could be derived from non-sensitive data because most data items are published in additive tables. Therefore, additional data values must be suppressed. These additional suppressed data values are commonly referred to as complementary suppressions. The objective adhered to by the Census Bureau in applying complementary suppressions is to minimize the sum of the data values chosen as complementary suppressions. Minimizing the cost incurred through complementary suppressions produces a publishable table with maximum data utility; that is, the greatest amount of usable data is provided. Furthermore, the Bureau uses complementary suppressions to ensure that a data user cannot estimate the value of a sensitive data cell within a predef'med interval. That is, when choosing complementary suppressions for some primary suppression with true value X, we ensure that it cannot be estimated within a smaller interval than [XL,X + U] where L is the amount of lower protection required by X, and U is the amount of upper protection required by X. Kelly, et al. (1991) discusses protection levels in greater detail. In recent years, the Economic Divisions of the Bureau have employed a cell suppression technique that utilizes network flow methodology. The origin of using graph theory in the disclosure avoidance area lies in Cox (1980), and Gusfield (1984). More recently, Cox, et al. (1986a) has outlined this methodology, and a more complete history is given in Greenberg (1990). A general outline of the minimum cost network flow problem and related methodology appears in Bazaraa & Jarvis (1977), and Gondran & Minoux (1984). The network flow system currently employed is implemented using the commercially available Minimum Cost Flow (MCF) program of Glover, Klingman and Mote. As described in its documentation, "MCF is a highly refined implementation of the upper bounded, revised primal simplex algorithm for linear programming." With this refined implementation, the primal simplex method can be performed directly on a network. Kennington and Helgason (1980) refer to this procedure as the "simplex on a graph" algorithm. Although M CF is computationally fast, it often oversuppresses due to the structure of the objective function (See Section 3). The ideal technique for choosing complementary suppressions is the integer programming routine outlined in Section 2. This routine, however, is computationally impractical for census tables. This paper discusses a hybrid technique outlined in Section 4 (using M CF and integer programming) that lessens the oversuppression problem without adding substantial computation time (see Section 5).