IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v47y2001i7p1008-1027.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.47.7.1008.9805
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.47.7.1008.9805?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Xiao-Bai Li & Sumit Sarkar, 2013. "Class-Restricted Clustering and Microperturbation for Data Privacy," Management Science, INFORMS, vol. 59(4), pages 796-812, April.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Codas, Andrés & Camponogara, Eduardo, 2012. "Mixed-integer linear optimization for optimal lift-gas allocation with well-separator routing," European Journal of Operational Research, Elsevier, vol. 217(1), pages 222-231.
    2. Wei-Kun Chen & Liang Chen & Mu-Ming Yang & Yu-Hong Dai, 2018. "Generalized coefficient strengthening cuts for mixed integer programming," Journal of Global Optimization, Springer, vol. 70(1), pages 289-306, January.
    3. Alves, Maria Joao & Climaco, Joao, 1999. "Using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 117(3), pages 565-577, September.
    4. Srinivasa, Anand V. & Wilhelm, Wilbert E., 1997. "A procedure for optimizing tactical response in oil spill clean up operations," European Journal of Operational Research, Elsevier, vol. 102(3), pages 554-574, November.
    5. Xiaoyi Gu & Santanu S. Dey & Jean-Philippe P. Richard, 2024. "Solving Sparse Separable Bilinear Programs Using Lifted Bilinear Cover Inequalities," INFORMS Journal on Computing, INFORMS, vol. 36(3), pages 884-899, May.
    6. Pourbabai, B. & Ashayeri, J. & Van Wassenhove, L.N., 1992. "Strategic marketing, production, and distribution planning of an integrated manufacturing system," Other publications TiSEM 16c2bacb-2c2b-427e-b429-c, Tilburg University, School of Economics and Management.
    7. B. Dietrich & L. Escudero & A. Garín & G. Pérez, 1993. "O(n) Procedures for identifying maximal cliques and non-dominated extensions of consecutive minimal covers and alternates," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 1(1), pages 139-160, December.
    8. Jose Manuel García, 2024. "New strategy for anti-loop formulations," OPSEARCH, Springer;Operational Research Society of India, vol. 61(4), pages 2346-2359, December.
    9. Amitabh Basu & Pierre Bonami & Gérard Cornuéjols & François Margot, 2011. "Experiments with Two-Row Cuts from Degenerate Tableaux," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 578-590, November.
    10. Eva K. Lee, 2004. "Generating Cutting Planes for Mixed Integer Programming Problems in a Parallel Computing Environment," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 3-26, February.
    11. Haque, Md Tabish & Hamid, Faiz, 2023. "Social distancing and revenue management—A post-pandemic adaptation for railways," Omega, Elsevier, vol. 114(C).
    12. Olivier Briant & Denis Naddef, 2004. "The Optimal Diversity Management Problem," Operations Research, INFORMS, vol. 52(4), pages 515-526, August.
    13. Escudero Bueno, Laureano F. & Garín Martín, María Araceli & Merino Maestre, María & Pérez Sainz de Rozas, Gloria, 2011. "A parallelizable algorithmic framework for solving large scale multi-stage stochastic mixed 0-1 problems under uncertainty," BILTOKI 1134-8984, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    14. Harjunkoski, Iiro & Westerlund, Tapio & Porn, Ray & Skrifvars, Hans, 1998. "Different transformations for solving non-convex trim-loss problems by MINLP," European Journal of Operational Research, Elsevier, vol. 105(3), pages 594-603, March.
    15. Ambros Gleixner & Leona Gottwald & Alexander Hoen, 2023. "P a PILO: A Parallel Presolving Library for Integer and Linear Optimization with Multiprecision Support," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1329-1341, November.
    16. Manfred Padberg, 2005. "Classical Cuts for Mixed-Integer Programming and Branch-and-Cut," Annals of Operations Research, Springer, vol. 139(1), pages 321-352, October.
    17. Xiangyong Li & Y. P. Aneja, 2012. "A Branch-and-Cut Approach for the Minimum-Energy Broadcasting Problem in Wireless Networks," INFORMS Journal on Computing, INFORMS, vol. 24(3), pages 443-456, August.
    18. Robert E. Bixby & Eva K. Lee, 1998. "Solving a Truck Dispatching Scheduling Problem Using Branch-and-Cut," Operations Research, INFORMS, vol. 46(3), pages 355-367, June.
    19. Aardal, K. & van Hoesel, C.P.M., 1995. "Polyhedral techniques in combinatorial optimization," Research Memorandum 014, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:47:y:2001:i:7:p:1008-1027. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.