A New Approach to Round Tabular Data

  • Juan José Salazar González
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4302)


Controlled Rounding is a technique to replace each cell value in a table with a multiple of a base number such that the new table satisfies the same equations as the original table. Statistical agencies prefer a solution where cell values already multiple of the base number remain unchanged, while the others are one of the two closest multiple of the base number (i.e., rounded up or rounded down). This solution is called zero-restricted rounding. Finding such a solution is a very complicated problems, and on some tables it may not exist. This paper presents a mathematical model and an algorithm to find a good-enough near-feasible solution for tables where a zero-restricted rounding is complicated. It also presents computational results showing the behavior of the proposal in practice.


Feasible Solution Base Number Protection Level Rounded Table Marginal Cell 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bacharach, M.: Matrix rounding problem. Management Science 9, 732–742 (1966)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Causey, B.D., Cox, L.H., Ernst, L.R.: Applications of transportation theory to statistical problems. Journal of the American Statistical Association 80, 903–909 (1985)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Cox, L.H.: Controlled rounding. INFOR 20, 423–432 (1982)MATHGoogle Scholar
  4. 4.
    Cox, L.H.: A constructive procedure for unbiased controlled rounding. Journal of the American Statistical Association 82, 520–524 (1987)MATHCrossRefGoogle Scholar
  5. 5.
    Cox, L.H., George, J.A.: Controlled rounding for tables with subtotals. Annals of Operations Research, 141–157 (1989)Google Scholar
  6. 6.
    Dalenius, T.: A simple procedure for controlled rounding. Statistisk Tidskrift 3, 202–208 (1981)Google Scholar
  7. 7.
    Fagan, J.T., Greenberg, B.V., Hemmig, R.: Controlled rounding of three dimensional tables. Technical report, Bureau of the Census, SRD/RR-88/02 (1988)Google Scholar
  8. 8.
    Fellegi, I.P.: Controlled random rounding. Survey Methodology, 123–133 (1975)Google Scholar
  9. 9.
    Moravek, J., Vlach, M.: On necessary conditions for the existence of the solution to the multi-index transportation problem. Operations Research, 542–545 (1967)Google Scholar
  10. 10.
    Salazar, J.J.: A unified mathematical programming framework for different statistical disclosure limitation methods. Operations Research 53(3), 819–829 (2005)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Salazar, J.J.: Controlled rounding and cell perturbation: Statistical disclosure limitation methods for tabular data. Mathematical Programming 105(2–3), 251–274 (2006)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Juan José Salazar González
    • 1
  1. 1.DEIOC, Faculty of MathematicsUniversity of La LagunaLa Laguna, TenerifeSpain

Personalised recommendations