Data Mining and Knowledge Discovery

, Volume 28, Issue 1, pp 65–91

The effect of homogeneity on the computational complexity of combinatorial data anonymization

  • Robert Bredereck
  • André Nichterlein
  • Rolf Niedermeier
  • Geevarghese Philip
Article

Abstract

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. 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. Complementing previous work, we introduce two new “data-driven” parameterizations for k-Anonymity—the number tin of different input rows and the number tout of different output rows—both modeling aspects of data homogeneity. We show that k-Anonymity is fixed-parameter tractable for the parameter tin, and that it is NP-hard even for tout = 2 and alphabet size four. Notably, our fixed-parameter tractability result implies that k-Anonymity can be solved in linear time when tin is a constant. Our computational hardness results also extend to the related privacy problems p-Sensitivity and -Diversity, while our fixed-parameter tractability results extend to p-Sensitivity and the usage of domain generalization hierarchies, where the entries are replaced by more general data instead of being completely suppressed.

Keywords

k-Anonymity p-Sensitivity -Diversity Domain generalization hierarchies Matrix modification problems Parameterized algorithmics Fixed-parameter tractability NP-hardness 

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References

  1. Aggarwal G, Feder T, Kenthapadi K, Motwani R, Panigrahy R, Thomas D, Zhu A (2005) Anonymizing tables. In: Proceedings of the 10th international conference on database theory (ICDT ’05), Springer, LNCS, vol 3363, pp 246–258Google Scholar
  2. Aggarwal G, Feder T, Kenthapadi K, Khuller S, Panigrahy R, Thomas D, Zhu A (2010) Achieving anonymity via clustering. ACM Trans Algorithms 6(3): 1–19CrossRefMathSciNetGoogle Scholar
  3. Blocki J, Williams R (2010) Resolving the complexity of some data privacy problems. In: Proceedings of the 37th international colloquium on automata, languages and programming (ICALP ’10), Springer, LNCS, vol 6199, pp 393–404Google Scholar
  4. Bonizzoni P, Della Vedova G, Dondi R (2011a) Anonymizing binary and small tables is hard to approximate. J Comb Optim 22(1): 97–119CrossRefMATHMathSciNetGoogle Scholar
  5. Bonizzoni P, Della Vedova G, Dondi R, Pirola Y (2011b) Parameterized complexity of k-anonymity: hardness and tractability. J Comb Optim (available online)Google Scholar
  6. Bredereck R, Nichterlein A, Niedermeier R, Philip G (2011) Pattern-guided data anonymization and clustering. In: Proceedings of the 36th international symposium mathematical foundations of computer science (MFCS ’11), Springer, LNCS, vol 6907, pp 182–193Google Scholar
  7. Campan A, Truta TM (2009) Data and structural k-anonymity in social networks. In: Proceedings of the 2nd ACM SIGKDD international workshop on privacy, security, and trust in KDD (PinKDD ’08), LNCS, vol 5456, Springer, pp 33–54Google Scholar
  8. Chakaravarthy VT, Pandit V, Sabharwal Y (2010) On the complexity of the k-anonymization problem. CoRR abs/1004.4729Google Scholar
  9. Dondi R, Mauri G, Zoppis I (2012) The ℓ-diversity problem: Tractability and approximability. Theor Comput Sci (available online)Google Scholar
  10. Downey RG, Fellows MR (1999) Parameterized Complexity. Springer,Google Scholar
  11. Dwork C (2011) A firm foundation for private data analysis. Commun ACM 54(1): 86–95CrossRefGoogle Scholar
  12. Evans PA, Wareham T, Chaytor R (2009) Fixed-parameter tractability of anonymizing data by suppressing entries. J Comb Optim 18(4): 362–375CrossRefMATHMathSciNetGoogle Scholar
  13. Fard AM, Wang K (2010) An effective clustering approach to web query log anonymization. In: Katsikas SK, Samarati P (eds) Proceedings of the international conference on security and cryptography (SECRYPT ’10), SciTePress, pp 109–119Google Scholar
  14. Fellows MR (2009) Towards fully multivariate algorithmics: some new results and directions in parameter ecology. In: Proceedings of the 20th international workshop on combinatorial algorithms (IWOCA ’09), Springer, LNCS, vol 5874, pp 2–10Google Scholar
  15. Flum J, Grohe M (2006) Parameterized complexity theory. Springer, BerlinGoogle Scholar
  16. Frank A, Asuncion A (2010) UCI machine learning repository. http://archive.ics.uci.edu/ml
  17. Fredkin E (1960) Trie memory. Commun ACM 3(9): 490–499CrossRefGoogle Scholar
  18. Fung BCM, Wang K, Chen R, Yu PS (2010) Privacy-preserving data publishing: a survey of recent developments. ACM Comput Surv 42(4): 14–11453CrossRefGoogle Scholar
  19. Gedik B, Liu L (2008) Protecting location privacy with personalized k-anonymity: architecture and algorithms. IEEE Trans Mobile Comput 7(1): 1–18CrossRefGoogle Scholar
  20. Gionis A, Tassa T (2009) k-anonymization with minimal loss of information. IEEE Trans Knowl Data Eng 21(2): 206–219CrossRefGoogle Scholar
  21. Gkoulalas-Divanis A, Kalnis P, Verykios VS (2010) Providing k-anonymity in location based services. ACM SIGKDD Explor Newsl 12: 3–10CrossRefGoogle Scholar
  22. Gruteser M, Grunwald D (2003) Anonymous usage of location-based services through spatial and temporal cloaking. In: Proceedings of the 1st international conference on mobile systems, applications and services (MOBISYS ’03), ACM, MobiSys ’03, pp 31–42Google Scholar
  23. Johnson DS (1987) The NP-completeness column: an ongoing guide. J Algorithms 8: 438–448CrossRefMATHMathSciNetGoogle Scholar
  24. Kenig B, Tassa T (2012) A practical approximation algorithm for optimal k-anonymity. Data Mining Knowl Discov 25: 134–168CrossRefMATHMathSciNetGoogle Scholar
  25. Komusiewicz C, Niedermeier R, Uhlmann J (2011) Deconstructing intractability—a multivariate complexity analysis of interval constrained coloring. J Discrete Algorithms 9: 137–151CrossRefMATHMathSciNetGoogle Scholar
  26. Li N, Li T, Venkatasubramanian S (2007) t-closeness: privacy beyond k-anonymity and l-diversity. In: Proceedings of the 23rd international conference on data engineering (ICDE ’07), IEEE, pp 106–115Google Scholar
  27. Machanavajjhala A, Kifer D, Gehrke J, Venkitasubramaniam M (2007) ℓ-diversity: privacy beyond k-anonymity. ACM Trans Knowl Discov Data 1(1): Article No. 3. doi:10.1145/1217299.1217302
  28. Meyerson A, Williams R (2004) On the complexity of optimal k-anonymity. In: Proceedings of the 23rd ACM SIGMOD-SIGACT-SIGART symposium on principles of database systems (PODS ’04), ACM, pp 223–228Google Scholar
  29. Monreale A, Andrienko G, Andrienko N, Giannotti F, Pedreschi D, Rinzivillo S, Wrobel S (2010) Movement data anonymity through generalization. Trans Data Privacy 3: 91–121MathSciNetGoogle Scholar
  30. Navarro-Arribas G, Torra V, Erola A, Castellà-Roca J (2012) User k-anonymity for privacy preserving data mining of query logs. Inf Process Manag 48(3): 476–487CrossRefGoogle Scholar
  31. Niedermeier R (2006) Invitation to fixed-parameter algorithms. Oxford University Press, OxfordCrossRefMATHGoogle Scholar
  32. Niedermeier R (2010) Reflections on multivariate algorithmics and problem parameterization. In: Proceedings of the 27th international symposium on theoretical aspects of computer science (STACS ’10), Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Leibniz international proceedings in informatics (LIPIcs), vol 5, pp 17–32Google Scholar
  33. Orlin J (1988) A faster strongly polynomial minimum cost flow algorithm. In: Proceedings of the 20th annual ACM symposium on theory of computing (STOC ’88), ACM, pp 377–387Google Scholar
  34. Park H, Shim K (2007) Approximate algorithms for k-anonymity. In: Proceedings of the international conference on management of data (SIGMOD ’07), ACM, SIGMOD ’07, pp 67–78Google Scholar
  35. Samarati P (2001) Protecting respondents identities in microdata release. IEEE Trans Knowl Data Eng 13(6): 1010–1027CrossRefGoogle Scholar
  36. Samarati P, Sweeney L (1998) Generalizing data to provide anonymity when disclosing information. In: Proceedings of the ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems (PODS ’98), ACM, pp 188–188Google Scholar
  37. Sweeney L (2000) Uniqueness of simple demographics in the U.S. population. Tech. rep., Carnegie Mellon University, School of Computer Science, Laboratory for International Data PrivacyGoogle Scholar
  38. Sweeney L (2002a) Achieving k-anonymity privacy protection using generalization and suppression. Int J Uncertain Fuzziness Knowl Based Syst 10(5): 571–588CrossRefMATHMathSciNetGoogle Scholar
  39. Sweeney L (2002b) k-Anonymity: a model for protecting privacy. Int J Uncertain Fuzziness Knowl Based Syst 10(5): 557–570CrossRefMATHMathSciNetGoogle Scholar
  40. Truta TM, Vinay B (2006) Privacy protection: p-sensitive k-anonymity property. In: Proceedings of the 22nd international conference on data engineering workshops (ICDE ’06), IEEE Computer Society, p 94Google Scholar
  41. Wong RCW, Li J, Fu AWC, Wang K (2006) (α, k)-anonymity: an enhanced k-anonymity model for privacy preserving data publishing. In: Proceedings of the 12th international conference on knowledge discovery and data mining (KDD ’06), ACM, pp 754–759Google Scholar
  42. Xiao X, Tao Y (2006) Anatomy: simple and effective privacy preservation. In: Proceedings of the 32nd international conference on very large data bases (VLDB ’06), ACM, pp 139–150Google Scholar
  43. Xiao X, Yi K, Tao Y (2010) The hardness and approximation algorithms for l-diversity. In: Proceedings of the 13th international conference on extending database technology (EDBT’ 10), ACM, pp 135–146Google Scholar
  44. Zhou B, Pei J (2011) The k-anonymity and l-diversity approaches for privacy preservation in social networks against neighborhood attacks. Knowl Inf Syst 28: 47–77CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Robert Bredereck
    • 1
  • André Nichterlein
    • 1
  • Rolf Niedermeier
    • 1
  • Geevarghese Philip
    • 2
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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