The k-Anonymity Problem Is Hard

  • Paola Bonizzoni
  • Gianluca Della Vedova
  • Riccardo Dondi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5699)


The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization recently proposed is the k-anonymity. This approach requires that the rows in a table are clustered in sets of size at least k and that all the rows in a cluster are related to the same tuple, after the suppression of some records. The problem has been shown to be NP-hard when the values are over a ternary alphabet, k = 3 and the rows length is unbounded. In this paper we give a lower bound on the approximation of two restrictions of the problem, when the records values are over a binary alphabet and k = 3, and when the records have length at most 8 and k = 4, showing that these restrictions of the problem are APX-hard.


Polynomial Time Vertex Cover Normal Solution Canonical Solution Minimum Vertex Cover 
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  1. 1.
    Aggarwal, G., Feder, T., Kenthapadi, K., Motwani, R., Panigrahy, R., Thomas, D., Zhu, A.: Anonymizing Tables. In: Eiter, T., Libkin, L. (eds.) ICDT 2005. LNCS, vol. 3363, pp. 246–258. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Alimonti, P., Kann, V.: Some APX-Completeness Results for Cubic Graphs. Theoretical Computer Science 237(1-2), 123–134 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    Gionis, A., Tassa, T.: k-Anonymization with Minimal Loss of Information. IEEE Trans. Knowl. Data Eng. 21(2), 206–219 (2009)CrossRefzbMATHGoogle Scholar
  5. 5.
    Park, H., Shim, K.: Approximate algorithms for k-Anonymity. In: Chan, C.Y., Ooi, B.C., Zhou, A. (eds.) ACM SIGMOD International Conference on Management of Data, pp. 67–78. ACM Press, New York (2007)Google Scholar
  6. 6.
    Samarati, P.: Protecting Respondents’ Identities in Microdata Release. IEEE Trans. Knowl. Data Eng. 13(6), 1010–1027 (2001)CrossRefGoogle Scholar
  7. 7.
    Samarati, P., Sweeney, L.: Generalizing Data to Provide Anonymity When Disclosing Information (Abstract). In: Seventeenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, p. 188. ACM Press, New York (1998)CrossRefGoogle Scholar
  8. 8.
    Sweeney, L.: k-Anonymity: a Model for Protecting Privacy. International Journal on Uncertainty, Fuzziness and Knowledge-based Systems 10(5), 557–570 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Paola Bonizzoni
    • 1
  • Gianluca Della Vedova
    • 2
  • Riccardo Dondi
    • 3
  1. 1.DISCoUniversità degli Studi di Milano-BicoccaMilanoItaly
  2. 2.Dipartimento di StatisticaUniversità degli Studi di Milano-BicoccaMilanoItaly
  3. 3.Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi CulturaliUniversità degli Studi di BergamoBergamoItaly

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