Mathematical Programming

, Volume 105, Issue 2–3, pp 583–603 | Cite as

Controlled rounding and cell perturbation: statistical disclosure limitation methods for tabular data

Article

Abstract

Rounding methods are common techniques in many statistical offices to protect sensitive information when publishing data in tabular form. Classical versions of these methods do not consider protection levels while searching patterns with minimum information loss, and therefore typically the so-called auditing phase is required to check the protection of the proposed patterns. This paper presents a mathematical model for the whole problem of finding a protected pattern with minimum loss of information, and proposes a branch-and-cut algorithm to solve it. It also describes a new methodology closely related to the classical Controlled Rounding methods but with several advantages. The new methodology is named Cell Perturbation and leads to a different optimization problem which is simpler to solve than the previous problem. This paper presents a cutting-plane algorithm for finding an exact solution of the new problem, which is a pattern guaranteeing the same protection level requirements but with smaller loss of information when compared with the classical Controlled Rounding optimal patterns. The auditing phase is unnecessary on the solutions generated by the two algorithms. The paper concludes with computational results on real-world instances and discusses a modification in the objective function to guarantee statistical properties in the solutions.

Keywords

Statistical disclosure Control Controlled rounding Integer linear Programming 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bacharach, M.: Matrix Rounding Problem. Management Sci. 9, 732–742 (1966)MathSciNetGoogle Scholar
  2. 2.
    Causey, B.D., Cox, L.H., Ernst, L.R.: Applications of Transportation Theory to Statistical Problems. J. American Statistical Association 80, 903–909 (1985)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cox, L.H., Ernst, L.R.: Controlled Rounding. INFOR 20, 423–432 (1982)MATHGoogle Scholar
  4. 4.
    Cox, L.H.: A Constructive Procedure for Unbiased Controlled Rounding. J. American Statistical Association 82, 520–524 (1987)MATHGoogle Scholar
  5. 5.
    Dandekar, R.A.: Maximum Utility-Minimum Information Loss Table Server Design for Statistical Disclosure Control of Tabular Data. In: Domingo-Ferrer, J. (ed.), Privacy in Statistical Databases. Lecture Notes in Computer Science 3050, Springer, 2004, pp. 121–135Google Scholar
  6. 6.
    Duncan, G.T., Fienberg, S.E., Krishnan, R., Padman, R., Roehrig, S.F.: ``Disclosure Limitation Methods and Information Loss for Tabular Data. In: Doyle, P., Lane, J., Theeuwes, J., Zayatz, L. (eds.), Confidentiality, Disclosure and Data Access: Theory and Practical Applications for Statistical Agencies. Elsevier Science, 2001, pp. 135–166Google Scholar
  7. 7.
    Fischetti, M., Salazar, J.J.: Computational Experience with the Controlled Rounding Problem in Statistical Disclosure Control. J. Official Stat. 14/4, 553–565 (1998)Google Scholar
  8. 8.
    Fischetti, M., Salazar, J.J.: Solving the Cell Suppression Problem on Tabular Data with Linear Constraints. Management Sci. 47, 1008–1026 (2000)Google Scholar
  9. 9.
    Fischetti, M., Salazar, J.J.: Partial Cell Suppression: a New Methodology for Statistical Disclosure Control. Stat. Comput. 13, 13–21 (2003)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Jewett, R.: Disclosure Analysis for the 1992 Economic Census. Internal report, U.S. Bureau of the Census, Washington, 1993Google Scholar
  11. 11.
    Kelly, J.P., Golden, B.L., Assad, A.A.: Using Simulated Annealing to Solve Controlled Rounding Problems. ORSA J. Comput. 2, 174–185 (1990)MATHGoogle Scholar
  12. 12.
    Kelly, J. P., Golden, B. L., Assad, A. A.: Large-Scale Controlled Rounding Using TABU Search with Strategic Oscillation. Ann. Oper. Res. 41, 69–84 (1993)CrossRefMATHGoogle Scholar
  13. 13.
    Salazar, J. J.: Controlled Rounding and Cell Perturbation: technical details. Internal report, University of La Laguna, Tenerife, 2004Google Scholar
  14. 14.
    Sande, G.: Automated Cell Suppression to preserve confidentiality of business statistics. Statistical Journal of the United Nations ECE 2, 1984, pp. 33–41Google Scholar
  15. 15.
    Willenborg, L.C.R.J., de Waal, T.: Elements of Statistical Disclosure Control. Lecture Notes in Statistics 155, Springer, 2001Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.DEIOC, Facultad de MatemáticasUniversidad de La LagunaTenerifeSpain

Personalised recommendations