Abstract
To protect sensitive information in a cross tabulated table, it is a common practice to suppress some of the cells. A linear combination of the suppressed cells is called a linear invariant if it has a unique feasible value. Because of this uniqueness, the information contained in a linear invariant is not protected. The minimal linear invariants are the most basic units of unprotected information. This paper establishes a fundamental correspondence between minimal linear invariants of a table and minimal edge cuts of a graph constructed from the table. As one of several consequences of this correspondence, a linear-time algorithm is obtained to find a set of minimal linear invariants that completely characterize the linear invariant information contained in individual rows and columns.
Supported in part by NSF Grant CCR-9101385.
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References
A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading, MA, 1974.
C. Berge. Graphs. North-Holland, New York, NY, second revised edition, 1985.
G. J. Brackstone, L. Chapman, and G. Sande. Protecting the confidentiality of individual statistical records in Canada. In Proceedings of the Conference of the European Statisticians 31st Plenary Session, Geneva, 1983.
T. H. Cormen, C. L. Leiserson, and R. L. Rivest. Introduction to Algorithms. MIT Press, Cambridge, MA, 1991.
L. H. Cox. Disclosure analysis and cell suppression. In Proceedings of the American Statistical Association, Social Statistics Section, pages 380–382, 1975.
L. H. Cox. Suppression methodology in statistics disclosure. In Proceedings of the American Statistical Association, Social Statistics Section, pages 750–755, 1977.
L. H. Cox. Automated statistical disclosure control. In Proceedings of the American Statistical Association, Survey Research Method Section, pages 177–182, 1978.
L. H. Cox. Suppression methodology and statistical disclosure control. Journal of the American Statistical Association, Theory and Method Section, 75:377–385, 1980.
L. H. Cox and G. Sande. Techniques for preserving statistical confidentiality. In Proceedings of the 42nd Session of the International Statistical Institute. the International Association of Survey Statisticians, 1979.
D. Denning. Cryptography and Data Security. Addison-Wesley, Reading, MA, 1982.
D. Gusfield. A graph theoretic approach to statistical data security. SIAM Journal on Computing, 17:552–571, 1988.
M. Y. Kao and D. Gusfield. Efficient detection and protection of information in cross tabulated tables I: Linear invariant test. SIAM Journal on Discrete. Mathematics, 6(3):460–476, 1993.
G. Sande. Towards automated disclosure analysis for establishment based statistics. Technical report, Statistics Canada, 1977.
G. Sande. A theorem concerning elementary aggregations in simple tables. Technical report, Statistics Canada, 1978.
G. Sande. Automated cell suppression to preserve confidentiality of business statistics. Statistical Journal of the United Nations, 2:33–41, 1984.
G. Sande. Confidentiality and polyhedra, an analysis of suppressed entries on cross tabulations. Technical report, Statistics Canada, unknown date.
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© 1995 Springer-Verlag Berlin Heidelberg
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Kao, MY. (1995). Minimal linear invariants. In: Kanchanasut, K., Lévy, JJ. (eds) Algorithms, Concurrency and Knowledge. ACSC 1995. Lecture Notes in Computer Science, vol 1023. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60688-2_32
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DOI: https://doi.org/10.1007/3-540-60688-2_32
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