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Solving L 1-CTA in 3D tables by an interior-point method for primal block-angular problems

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Abstract

The purpose of the field of statistical disclosure control is to avoid that confidential information could be derived from statistical data released by, mainly, national statistical agencies. Controlled tabular adjustment (CTA) is an emerging technique for the protection of statistical tabular data. Given a table with sensitive information, CTA looks for the closest safe table. In this work we focus on CTA for three-dimensional tables using the L 1 norm for the distance between the original and protected tables. Three L 1-CTA models are presented, giving rise to six different primal block-angular structures of the constraint matrices. The resulting linear programming problems are solved by a specialized interior-point algorithm for this constraints structure which solves the normal equations by a combination of Cholesky factorization and preconditioned conjugate gradients (PCG). In the past this algorithm was shown to be one of the most efficient approaches for some classes of block-angular problems. The effect of quadratic regularizations is also analyzed, showing that for three of the six primal block-angular structures the performance of PCG is guaranteed to improve. Computational results are reported for a set of large instances, which provide linear optimization problems of up to 50 million variables and 25 million constraints. The specialized interior-point algorithm is compared with the state-of-the-art barrier solver of the CPLEX 12.1 package, showing to be a more efficient choice for very large L 1-CTA instances.

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Acknowledgements

This work has been supported by grants MTM2009-08747 of the Spanish Ministry of Science and Innovation, and SGR-2009-1122 of the Government of Catalonia. The authors thank the anonymous referees for their valuable suggestions.

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Authors and Affiliations

  1. Dept. of Statistics and Operations Research, Universitat Politècnica de Catalunya, Jordi Girona 1-3, 08034, Barcelona, Catalonia, Spain

    Jordi Castro

  2. Statistics and Operations Research unit, Dept. of Chemical Engineering, Universitat Rovira i Virgili, Avda. Països Catalans 26, 43007, Tarragona, Catalonia, Spain

    Jordi Cuesta

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  1. Jordi Castro
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  2. Jordi Cuesta
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Correspondence to Jordi Castro.

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Castro, J., Cuesta, J. Solving L 1-CTA in 3D tables by an interior-point method for primal block-angular problems. TOP 21, 25–47 (2013). https://doi.org/10.1007/s11750-011-0247-z

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  • DOI: https://doi.org/10.1007/s11750-011-0247-z

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