Abstract
Methods for the protection of statistical tabular data—as controlled tabular adjustment, cell suppression, or controlled rounding—need to solve several linear programming subproblems. For large multidimensional linked and hierarchical tables, such subproblems turn out to be computationally challenging. One of the techniques used to reduce the solution time of mathematical programming problems is to exploit the constraints structure using some specialized algorithm. Two of the most usual structures are block-angular matrices with either linking rows (primal block-angular structure) or linking columns (dual block-angular structure). Although constraints associated to tabular data have intrinsically a lot of structure, current software for tabular data protection neither detail nor exploit it, and simply provide a single matrix, or at most a set of smallest submatrices. We provide in this work an efficient tool for the automatic detection of primal or dual block-angular structure in constraints matrices. We test it on some of the complex CSPLIB instances, showing that when the number of linking rows or columns is small, the computational savings are significant.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benders, J.F.: Partitioning procedures for solving mixed-variables programming problems. Computational Management Science 2, 3–19 (2005)
Bixby, R.E.: Solving real-world linear programs: a decade and more of progress. Operations Research 50, 3–15 (2002)
Bradley, S.P., Hax, A.C., Magnanti, T.L.: Applied Mathematical Programming. Addison-Wesley, Reading (1977)
Castro, J.: Network flows heuristics for complementary cell suppression: an empirical evaluation and extensions. In: Domingo-Ferrer, J. (ed.) Inference Control in Statistical Databases. LNCS, vol. 2316, pp. 59–73. Springer, Berlin (2002)
Castro, J.: Quadratic interior-point methods in statistical disclosure control. Computational Management Science 2, 107–121 (2005)
Castro, J.: Minimum-distance controlled perturbation methods for large-scale tabular data protection. European Journal of Operational Research 171, 39–52 (2006)
Castro, J.: A shortest paths heuristic for statistical disclosure control in positive tables. To appear in INFORMS Journal on Computing. Available as Research Report DR 2004/10 Dept. of Statistics and Operations Research, Universitat Politècnica de Catalunya (2004)
Castro, J.: An interior-point approach for primal block-angular problems. To appear in Computational Optimization and Applications (2007). Available as Research Report DR 2005/20 Dept. of Statistics and Operations Research, Universitat Politècnica de Catalunya (2005)
Cox, L.H.: Network models for complementary cell suppression. J. Am. Stat. Assoc. 90, 1453–1462 (1995)
Cox, L.H., George, J.A.: Controlled rounding for tables with subtotals. Annals of Operations Research 20, 141–157 (1989)
Dandekar, R.A.: Personal communication (2005)
Dandekar, R.A., Cox, L.H.: Synthetic tabular Data: an alternative to complementary cell suppression, Energy Information Administration, U.S, manuscript
Dantzig, G.B., Wolfe, P.: Decomposition principle for linear programs. Operations Research 8, 101–111 (1960)
Fischetti, M., Salazar, J.J.: Solving the cell suppression problem on tabular data with linear constraints. Management Science 47, 1008–1026 (2001)
Gondzio, J., Sarkissian, R.: Parallel interior point solver for structured linear programs. Mathematical Programming 96, 561–584 (2003)
Hu, Y.F., Maguire, K.C.F., Blake, R.J.: A multilevel unsymmetric matrix ordering algorithm for parallel process simulation. Computers and Chemical Engineering 23, 1631–1647 (2000)
Hundepool, A.: The CASC project. In: Domingo-Ferrer, J. (ed.) Inference Control in Statistical Databases. LNCS, vol. 2316, pp. 172–180. Springer, Berlin (2002)
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on scientific Computing 20, 359–392 (1999)
Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Systems Technical Journal 49, 291–308 (1970)
Salazar, J.J.: Controlled rounding and cell perturbation: statistical disclosure limitation methods for tabular data. Mathematical Programming 105, 583–603 (2006)
Wright, S.J.: Primal-Dual Interior-Point Methods. SIAM, Philadelphia (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Castro, J., Baena, D. (2006). Automatic Structure Detection in Constraints of Tabular Data. In: Domingo-Ferrer, J., Franconi, L. (eds) Privacy in Statistical Databases. PSD 2006. Lecture Notes in Computer Science, vol 4302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11930242_2
Download citation
DOI: https://doi.org/10.1007/11930242_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49330-3
Online ISBN: 978-3-540-49332-7
eBook Packages: Computer ScienceComputer Science (R0)