Parameterized Complexity of k-Anonymity: Hardness and Tractability

  • Paola Bonizzoni
  • Gianluca Della Vedova
  • Riccardo Dondi
  • Yuri Pirola
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6460)

Abstract

The problem of publishing personal data without giving up privacy is becoming increasingly important. A precise formalization that has been recently proposed is the k-anonymity, where the rows of a table are partitioned in clusters of size at least k and all rows in a cluster become the same tuple after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is hard even when the stored values are over a binary alphabet or the table consists of a bounded number of columns. In this paper we study how the complexity of the problem is influenced by different parameters. First we show that the problem is W[1]-hard when parameterized by the value of the solution (and k). Then we exhibit a fixed-parameter algorithm when the problem is parameterized by the number of columns and the number of different values in any column.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aggarwal, G., Feder, T., Kenthapadi, K., Khuller, S., Panigrahy, R., Thomas, D., Zhu, A.: Achieving anonymity via clustering. In: Vansummeren, S. (ed.) PODS, pp. 153–162. ACM, New York (2006)Google Scholar
  2. 2.
    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 (2005)CrossRefGoogle Scholar
  3. 3.
    Aggarwal, G., Kenthapadi, K., Motwani, R., Panigrahy, R., Thomas, D., Zhu, A.: Approximation algorithms for k-anonymity. J. Privacy Technology (2005)Google Scholar
  4. 4.
    Blocki, J., Williams, R.: Resolving the complexity of some data privacy problems. In: Abramsky, S., Gavoille, C., Kirchner, C., auf der Heide, F.M., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 393–404. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Bonizzoni, P., Della Vedova, G., Dondi, R.: The k-anonymity problem is hard. In: Kutylowski, M., Gebala, M., Charatonik, W. (eds.) FCT 2009. LNCS, vol. 5699, pp. 26–37. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Chaytor, R., Evans, P.A., Wareham, T.: Fixed-parameter tractability of anonymizing data by suppressing entries. J. Comb. Optim. 18(4), 362–375 (2009)CrossRefMATHGoogle Scholar
  7. 7.
    Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  8. 8.
    Downey, R.G., Fellows, M.R.: Fixed-parameter tractability and completeness ii: On completeness for W[1]. Theoretical Computer Science 141, 109–131 (1995)CrossRefMATHGoogle Scholar
  9. 9.
    Du, W., Eppstein, D., Goodrich, M.T., Lueker, G.S.: On the approximability of geometric and geographic generalization and the min-max bin covering problem. In: Dehne, F.K.H.A., Gavrilova, M.L., Sack, J.R., Tóth, C.D. (eds.) WADS 2009. LNCS, vol. 5664, pp. 242–253. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Gionis, A., Tassa, T.: k-anonymization with minimal loss of information. TKDD 21(2), 206–219 (2009)MATHGoogle Scholar
  11. 11.
    Meyerson, A., Williams, R.: On the complexity of optimal k-anonymity. In: Deutsch, A. (ed.) PODS, pp. 223–228. ACM, New York (2004)Google Scholar
  12. 12.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)CrossRefMATHGoogle Scholar
  13. 13.
    Park, H., Shim, K.: Approximate algorithms for k-anonymity. In: Chan, C.Y., Ooi, B.C., Zhou, A. (eds.) SIGMOD Conference, pp. 67–78. ACM, New York (2007)Google Scholar
  14. 14.
    Samarati, P.: Protecting respondents’ identities in microdata release. IEEE Trans. Knowl. Data Eng. 13, 1010–1027 (2001)CrossRefGoogle Scholar
  15. 15.
    Samarati, P., Sweeney, L.: Generalizing data to provide anonymity when disclosing information (abstract). In: PODS, p. 188. ACM, New York (1998)Google Scholar
  16. 16.
    Schwartz, J., Steger, A., Weißl, A.: Fast algorithms for weighted bipartite matching. In: Nikoletseas, S.E. (ed.) WEA 2005. LNCS, vol. 3503, pp. 476–487. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Sweeney, L.: k-anonymity: a model for protecting privacy. International Journal on Uncertainty, Fuzziness and Knowledge-based Systems 10, 557–570 (2002)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Paola Bonizzoni
    • 1
  • Gianluca Della Vedova
    • 2
  • Riccardo Dondi
    • 3
  • Yuri Pirola
    • 1
  1. 1.DISCoUniv. Milano-BicoccaItaly
  2. 2.Dip. StatisticaUniv. Milano-BicoccaItaly
  3. 3.Dipartimento di Scienze dei Linguaggi, della Comunicazione e degli Studi CulturaliUniversità degli Studi di BergamoItaly

Personalised recommendations