J. Domingo-Ferrer and V. Torra (Eds.): PSD 2004, LNCS 3050, pp. 58–72, 2004.  Springer-Verlag Berlin Heidelberg 2004 Getting the Best Results in Controlled Rounding with the Least Effort Juan-José Salazar-González 1 , Philip Lowthian 2 , Caroline Young 2 , Giovanni Merola 2 , Stephen Bond 2 , and David Brown 2 1 Department of Statistics, Operational Research & Computer Science University of La Laguna, Tenerife, Spain 2 Statistical Disclosure Control Centre, Methodology Group Office for National Statistics, London, UK Abstract. This paper describes computational experiments with an algorithm for control-rounding any series of linked tables such as typically occur in offi- cial statistics, for the purpose of confidentiality protection of the individual con- tributors to the tables. The resulting tables consist only of multiples of the specified rounding base, are additive, and have specified levels of confidential- ity protection. Computational experiments are presented demonstrating the con- siderable power of the program for control-rounding very large tables or series of linked tables. Heuristic approaches to problematic cases are presented, as are procedures for specifying the input to the program. The statistical properties of the rounding perturbations are described, and a method of overcoming statisti- cal bias in the rounding algorithm is demonstrated. 1 Introduction Rounding techniques involve the replacement of the original data by multiples of a given rounding base. Rounding (e.g. to the nearest integer) has been used in science for presentational purposes for many centuries. Random and deterministic rounding has been used as a confidentiality protection tool by national statistics instititues in tabular data for decades (see e.g. Nargundkar and Saveglund [11], Ryan [14], Willen- borg and de Waal [15]). Unfortunately naive rounding frequently destroys additivity in tables. Controlled rounding has the desirable feature that the rounded tables are additive i.e. the values in the marginal cells coincide with those calculated by adding the relevant interior cells. As a general numerical technique, controlled (or matrix) rounding is not new: solutions were provided by Bacharach [1] as early as 1966. Con- trolled rounding was, however, developed and promoted as a serious technique for official statistics by Cox and coworkers in the 1980s (Cox and Ernst [3], Causey et al [2], Cox [4]). Further work on computational aspects was done by other workers (e.g. Kelly, Golden, Assad and Baker [8,9,10]). One difficulty discovered by Causey et al [2] was the existence of three dimen- sional tables for which classical (zero-restricted) controlled rounding was impossible. In zero-restricted controlled rounding, cell entries that are already a multiple of the rounding base are not changed, and other entries can only move to an adjacent multi- ple of the rounding base. Fischetti and Salazar-González [6] overcame this problem