The Effect of Homogeneity on the Complexity of k-Anonymity

  • Robert Bredereck
  • André Nichterlein
  • Rolf Niedermeier
  • Geevarghese Philip
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6914)


The NP-hard k-Anonymity problem asks, given an n ×m-matrix M over a fixed alphabet and an integer s > 0, whether M can be made k-anonymous by suppressing (blanking out) at most s entries. A matrix M is said to be k-anonymous if for each row r in M there are at least k–1 other rows in M which are identical to r. Complementing previous work, we introduce two new “data-driven” parameterizations for k-Anonymity—the number \({t_{\textrm{in}}}\) of different input rows and the number \(t_{\textrm{out}}\) of different output rows—both modeling aspects of data homogeneity. We show that k-Anonymity is fixed-parameter tractable for the parameter \({t_{\textrm{in}}}\), and it is NP-hard even for \({t_{\textrm{out}}} = 2\) and alphabet size four. Notably, our fixed-parameter tractability result implies that k-Anonymity can be solved in linear time when \({t_{\textrm{in}}}\) is a constant. Our results also extend to some interesting generalizations of k-Anonymity.


Parameterized Complexity Output Type Alphabet Size Combine Parameter Partition Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aggarwal, G., Feder, T., Kenthapadi, K., Khuller, S., Panigrahy, R., Thomas, D., Zhu, A.: Achieving anonymity via clustering. ACM Trans. Algorithms 6(3), 1–19 (2010)MathSciNetCrossRefMATHGoogle 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.
    Blocki, J., Williams, R.: Resolving the complexity of some data privacy problems. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 393–404. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Bonizzoni, P., DellaVedova, G., Dondi, R.: Anonymizing binary and small tables is hard to approximate. J. Comb. Optim. 22, 97–119 (2011)MathSciNetMATHGoogle Scholar
  5. 5.
    Bonizzoni, P., Della Vedova, G., Dondi, R., Pirola, Y.: Parameterized complexity of k-anonymity: Hardness and tractability. In: Iliopoulos, C.S., Smyth, W.F. (eds.) IWOCA 2010. LNCS, vol. 6460, pp. 242–255. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Bredereck, R., Nichterlein, A., Niedermeier, R., Philip, G.: Pattern-guided data anonymization and clustering. In: Proc. 36th MFCS. LNCS. Springer, Heidelberg (to appear, 2011)Google Scholar
  7. 7.
    Chakaravarthy, V.T., Pandit, V., Sabharwal, Y.: On the complexity of the k-anonymization problem. CoRR, abs/1004.4729 (2010)Google Scholar
  8. 8.
    Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  9. 9.
    Dwork, C.: A firm foundation for private data analysis. Commun. ACM 54, 86–95 (2011)CrossRefGoogle Scholar
  10. 10.
    Evans, P.A., Wareham, T., Chaytor, R.: Fixed-parameter tractability of anonymizing data by suppressing entries. J. Comb. Optim. 18(4), 362–375 (2009)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Fard, A.M., Wang, K.: An effective clustering approach to web query log anonymization. In: Proc. SECRYPT, pp. 109–119. SciTePress (2010)Google Scholar
  12. 12.
    Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Heidelberg (2006)MATHGoogle Scholar
  13. 13.
    Fredkin, E.: Trie memory. Commun. ACM 3(9), 490–499 (1960)CrossRefGoogle Scholar
  14. 14.
    Fung, B.C.M., Wang, K., Chen, R., Yu, P.S.: Privacy-preserving data publishing: A survey of recent developments. ACM Comput. Surv. 42(4), 14:1–14:53 (2010)Google Scholar
  15. 15.
    Johnson, D.S.: The NP-completeness column: An ongoing guide. J. Algorithms 8, 438–448 (1987)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Deconstructing intractability–A multivariate complexity analysis of interval constrained coloring. J. Discrete Algorithms 9, 137–151 (2011)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Li, N., Li, T., Venkatasubramanian, S.: t-closeness: Privacy beyond k-anonymity and l-diversity. In: Proc. 23rd ICDE, pp. 106–115. IEEE, Los Alamitos (2007)Google Scholar
  18. 18.
    Machanavajjhala, A., Kifer, D., Gehrke, J., Venkitasubramaniam, M.: ℓ-diversity: Privacy beyond k-anonymity. ACM Trans. Knowl. Discov. Data 1, 52 (2007)CrossRefGoogle Scholar
  19. 19.
    Meyerson, A., Williams, R.: On the complexity of optimal k-anonymity. In: Proc. 23rd PODS, pp. 223–228. ACM, New York (2004)Google Scholar
  20. 20.
    Niedermeier, R.: Invitation to Fixed-Parameter Algorithms. Oxford University Press, Oxford (2006)CrossRefMATHGoogle Scholar
  21. 21.
    Niedermeier, R.: Reflections on multivariate algorithmics and problem parameterization. In: Proc. 27th STACS. LIPIcs, vol. 5, pp. 17–32. IBFI, Dagstuhl (2010)Google Scholar
  22. 22.
    Orlin, J.: A faster strongly polynomial minimum cost flow algorithm. In: Proc. 20th STOC, pp. 377–387. ACM, New York (1988)Google Scholar
  23. 23.
    Sweeney, L.: Achieving k-anonymity privacy protection using generalization and suppression. IJUFKS 10(5), 571–588 (2002)MathSciNetMATHGoogle Scholar
  24. 24.
    Sweeney, L.: k-anonymity: A model for protecting privacy. IJUFKS 10(5), 557–570 (2002)MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Robert Bredereck
    • 1
  • André Nichterlein
    • 1
  • Rolf Niedermeier
    • 1
  • Geevarghese Philip
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany
  2. 2.The Institute of Mathematical SciencesChennaiIndia

Personalised recommendations