A Shortest-Paths Heuristic for Statistical Data Protection in Positive Tables

Abstract

i ' N ational statistical agencies (NSAs) routinely release large amounts of tabular information. Prior to dissemination, tabular data need to be processed to avoid disclosure of individual corifidential information. Cell suppression is one of the most widely used techniques by NSAs. Optimal procedures for cell suppression are computationally expensive with large real-world data sets, so heuristic procedures are used. Most heuristics for positive tables (i.e., cell values are normegative) rely on the solution of minimum-cost network-flows subproblems. A very efficient heuristic based on shortest paths already exists, but it is only appropriate for general tables (i.e., cell values can be either positive or negative), whereas in practice most tables are positive. We present a method that sensibly combines and improves previous approaches, overcoming some of their drawbacks: it is designed for positive tables and requires only the solution of shortest-path subproblems-therefore being much more efficient than other network-flows heuristics. We report extensive computational experience in the solution of randomly generated and real-world instances, comparing the heuristic with alternative procedures. The results show that the method, currently included in a software package for statistical data protection, fits NSA needs: it is extremely efficient and provides good solutions.

Perspective Reformulations of the CTA Problem with L2 Distances

“…Hierarchical instances were obtained with a generator of 1H2D synthetic tables [4] that was retrieved from http://www-eio.upc.es/~jcastro/generators_csp.html. This is a relevant class of instances, since a significant fraction of the tables released by NSAs are 1H2D.…”

“…Clearly, nonperturbative approaches are more rigid than perturbative ones. Furthermore, the most widely used nonperturbative approach, cell suppression [23,10,4], requires the solution of large-scale optimization problems to identify the optimal set of cells to be suppressed. It is perhaps not surprising, therefore, that perturbative approaches are being considered as emerging technologies for tabular data protection.…”

Pre-processing Optimisation Applied to the Classical Integer Programming Model for Statistical Disclosure Control

“…he is not aware which suppressed cells are primary nor secondary but he knows that there is a number of suppressed cells in the table and their location (disclosure pattern). As each table has row and column totals, often referred to as marginals, the external attacker is able to calculate lower and upper bounds, feasibility range, for each of the suppressed cells by solving a set of linear constraint equations [1] [6].…”

“…A statistical table with marginal totals can be represented as a set of cells, please see details of the model in [1] and [6], a i , i = 1, ..., n, satisfying m linear constraint equations such that M a = 0, where M ij has one of the values…”

“…The statistical agency will provide lower and upper protection levels (lpl and upl) for each cell in P such that an external attacker must not be able to calculate a p within the range lpl p to upl p . For a p to be safe a p ≤ lpl p and a p ≥ upl p where a p is the lower bound and a p the upper bound of the feasible range that the external attacker can calculate for a p if only the primary cells P have been suppressed [1].…”