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Solving the Cell Suppression Problem on Tabular Data with Linear Constraints

Author

Listed:
  • Matteo Fischetti

    (DEI, University of Padova, Italy)

  • Juan José Salazar

    (DEIOC, University of La Laguna, Spain)

Abstract

Cell suppression is a widely used technique for protecting sensitive information in statistical data presented in tabular form. Previous works on the subject mainly concentrate on 2- and 3-dimensional tables whose entries are subject to marginal totals. In this paper we address the problem of protecting sensitive data in a statistical table whose entries are linked by a generic system of linear constraints. This very general setting covers, among others, k-dimensional tables with marginals as well as the so-called hierarchical and linked tables that are very often used nowadays for disseminating statistical data. In particular, we address the optimization problem known in the literature as the (secondary) Cell Suppression Problem, in which the information loss due to suppression has to be minimized. We introduce a new integer linear programming model and outline an enumerative algorithm for its exact solution. The algorithm can also be used as a heuristic procedure to find near-optimal solutions. Extensive computational results on a test-bed of 1,160 real-world and randomly generated instances are presented, showing the effectiveness of the approach. In particular, we were able to solve to proven optimality 4-dimensional tables with marginals as well as linked tables of reasonable size (to our knowledge, tables of this kind were never solved optimally by previous authors).

Suggested Citation

  • Matteo Fischetti & Juan José Salazar, 2001. "Solving the Cell Suppression Problem on Tabular Data with Linear Constraints," Management Science, INFORMS, vol. 47(7), pages 1008-1027, July.
    • Handle: RePEc:inm:ormnsc:v:47:y:2001:i:7:p:1008-1027
    DOI: 10.1287/mnsc.47.7.1008.9805
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    References listed on IDEAS

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    1. Harlan Crowder & Ellis L. Johnson & Manfred Padberg, 1983. "Solving Large-Scale Zero-One Linear Programming Problems," Operations Research, INFORMS, vol. 31(5), pages 803-834, October.
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    Citations

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    Cited by:

    1. Juan-José Salazar-González, 2005. "A Unified Mathematical Programming Framework for Different Statistical Disclosure Limitation Methods," Operations Research, INFORMS, vol. 53(5), pages 819-829, October.
    2. Castro, Jordi, 2012. "Recent advances in optimization techniques for statistical tabular data protection," European Journal of Operational Research, Elsevier, vol. 216(2), pages 257-269.
    3. Jordi Castro & Antonio Frangioni & Claudio Gentile, 2014. "Perspective Reformulations of the CTA Problem with L 2 Distances," Operations Research, INFORMS, vol. 62(4), pages 891-909, August.
    4. Xiao-Bai Li & Sumit Sarkar, 2013. "Class-Restricted Clustering and Microperturbation for Data Privacy," Management Science, INFORMS, vol. 59(4), pages 796-812, April.
    5. Daniel Baena & Jordi Castro & Antonio Frangioni, 2020. "Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy," Management Science, INFORMS, vol. 66(7), pages 3051-3068, July.
    6. Zhang, Sumei & Guldmann, Jean-Michel, 2009. "Estimating suppressed data in regional economic databases: A goal-programming approach," European Journal of Operational Research, Elsevier, vol. 192(2), pages 521-537, January.
    7. Robert Garfinkel & Ram Gopal & Steven Thompson, 2007. "Releasing Individually Identifiable Microdata with Privacy Protection Against Stochastic Threat: An Application to Health Information," Information Systems Research, INFORMS, vol. 18(1), pages 23-41, March.
    8. Jordi Castro, 2007. "A Shortest-Paths Heuristic for Statistical Data Protection in Positive Tables," INFORMS Journal on Computing, INFORMS, vol. 19(4), pages 520-533, November.
    9. Castro, Jordi, 2006. "Minimum-distance controlled perturbation methods for large-scale tabular data protection," European Journal of Operational Research, Elsevier, vol. 171(1), pages 39-52, May.
    10. Haibing Lu & Jaideep Vaidya & Vijayalakshmi Atluri & Yingjiu Li, 2015. "Statistical Database Auditing Without Query Denial Threat," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 20-34, February.

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