Improved Upper and Lower Bound Heuristics for Degree Anonymization in Social Networks

  • Sepp Hartung
  • Clemens Hoffmann
  • André Nichterlein
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8504)


Motivated by a strongly growing interest in anonymizing social network data, we investigate the NP-hard Degree Anonymization problem: given an undirected graph, the task is to add a minimum number of edges such that the graph becomes k-anonymous. That is, for each vertex there have to be at least k − 1 other vertices of exactly the same degree. The model of degree anonymization has been introduced by Liu and Terzi [ACM SIGMOD’08], who also proposed and evaluated a two-phase heuristic. We present an enhancement of this heuristic, including new algorithms for each phase which significantly improve on the previously known theoretical and practical running times. Moreover, our algorithms are optimized for large-scale social networks and provide upper and lower bounds for the optimal solution. Notably, on about 26 % of the real-world data we provide (provably) optimal solutions; whereas in the other cases our upper bounds significantly improve on known heuristic solutions.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barabási, A., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Berthomé, P., Lalande, J.-F., Levorato, V.: Implementation of exponential and parametrized algorithms in the AGAPE project. CoRR, abs/1201.5985 (2012)Google Scholar
  3. 3.
    Casas-Roma, J., Herrera-Joancomartí, J., Torra, V.: An algorithm for k-degree anonymity on large networks. In: Proc. ASONAM 2013, pp. 671–675. ACM Press (2013)Google Scholar
  4. 4.
    Chester, S., Gaertner, J., Stege, U., Venkatesh, S.: Anonymizing subsets of social networks with degree constrained subgraphs. In: Proc. ASONAM 2012, pp. 418–422. IEEE Computer Society (2012)Google Scholar
  5. 5.
    DIMACS 2012. Graph partitioning and graph clustering. 10th DIMACS challenge (2012), (accessed April 2012)
  6. 6.
    Easley, D., Kleinberg, J.: Networks, Crowds, and Markets. Cambridge University Press (2010)Google Scholar
  7. 7.
    Erdős, P., Gallai, T.: Graphs with prescribed degrees of vertices. Math. Lapok 11, 264–274 (1960) (in Hungarian)Google Scholar
  8. 8.
    Fung, B.C.M., Wang, K., Chen, R., Yu, P.S.: Privacy-preserving data publishing: A survey of recent developments. ACM Computing Surveys 42(4), 14:1–14:53 (2010)Google Scholar
  9. 9.
    Hartung, S., Nichterlein, A., Niedermeier, R., Suchý, O.: A refined complexity analysis of degree anonymization in graphs. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds.) ICALP 2013, Part II. LNCS, vol. 7966, pp. 594–606. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  10. 10.
    Hartung, S., Hoffmann, C., Nichterlein, A.: Improved upper and lower bound heuristics for degree anonymization in social networks. CoRR, abs/1402.6239 (2014)Google Scholar
  11. 11.
    Liu, K., Terzi, E.: Towards identity anonymization on graphs. In: Proc. SIGMOD 2008, pp. 93–106. ACM (2008)Google Scholar
  12. 12.
    Lu, X., Song, Y., Bressan, S.: Fast identity anonymization on graphs. In: Liddle, S.W., Schewe, K.-D., Tjoa, A.M., Zhou, X. (eds.) DEXA 2012, Part I. LNCS, vol. 7446, pp. 281–295. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Samarati, P.: Protecting respondents identities in microdata release. IEEE Transactions on Knowledge and Data Engineering 13(6), 1010–1027 (2001)CrossRefGoogle Scholar
  14. 14.
    Samarati, P., Sweeney, L.: Generalizing data to provide anonymity when disclosing information. In: Proc. PODS 1998, pp. 188–188. ACM (1998)Google Scholar
  15. 15.
    Sweeney, L.: k-anonymity: A model for protecting privacy. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10(5), 557–570 (2002)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Thompson, B., Yao, D.: The union-split algorithm and cluster-based anonymization of social networks. In: Proc. 4th ASIACCS 2009, pp. 218–227. ACM (2009)Google Scholar
  17. 17.
    Tripathi, A., Vijay, S.: A note on a theorem of Erdös & Gallai. Discrete Math. 265(1-3), 417–420 (2003)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Zhou, B., Pei, J.: The k-anonymity and l-diversity approaches for privacy preservation in social networks against neighborhood attacks. Knowledge and Information Systems 28(1), 47–77 (2011)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Zhou, B., Pei, J., Luk, W.: A brief survey on anonymization techniques for privacy preserving publishing of social network data. ACM SIGKDD Explorations Newsletter 10(2), 12–22 (2008)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Sepp Hartung
    • 1
  • Clemens Hoffmann
    • 1
  • André Nichterlein
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

Personalised recommendations