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Column generation bounds for numerical microaggregation

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Abstract

The biggest challenge when disclosing private data is to share information contained in databases while protecting people from being individually identified. Microaggregation is a family of methods for statistical disclosure control. The principle of microaggregation is that confidentiality rules permit the publication of individual records if they are partitioned into groups of size larger or equal to a fixed threshold value, where none is more representative than the others in the same group. The application of such rules leads to replacing individual values by those computed from small groups (microaggregates), before data publication. This work proposes a column generation algorithm for numerical microaggregation in which its pricing problem is solved by a specialized branch-and-bound. The algorithm is able to find, for the first time, lower bounds for instances of three real-world datasets commonly used in the literature. Furthermore, new best known solutions are obtained for these instances by means of a simple heuristic method with the columns generated.

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Acknowledgments

Research of the first author has been supported by the National Council for Scientific and Technological Development—CNPq/Brazil Grant Numbers 474231/2010-0 and 305070/2011-8. The authors also thank Prof. Costas Panagiotakis for providing the Tarragona, Census and Eia datasets.

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Authors and Affiliations

  1. Universidade Federal do Rio Grande do Norte, Campus Universitário s/n, Natal, RN, 59072-970, Brazil

    Daniel Aloise, Caroline Rocha & Éverton Santi

  2. GERAD and HEC Montréal, 3000, Chemin de la Côte-Sainte-Catherine, Montreal, QC, H3T 2A7, Canada

    Pierre Hansen

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  1. Daniel Aloise
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  2. Pierre Hansen
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  3. Caroline Rocha
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  4. Éverton Santi
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Correspondence to Daniel Aloise.

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Aloise, D., Hansen, P., Rocha, C. et al. Column generation bounds for numerical microaggregation. J Glob Optim 60, 165–182 (2014). https://doi.org/10.1007/s10898-014-0149-3

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