Abstract
We formally study two methods for data sanitation that have been used extensively in the database community: k-anonymity and ℓ-diversity. We settle several open problems concerning the difficulty of applying these methods optimally, proving both positive and negative results:
-
2-anonymity is in P.
-
The problem of partitioning the edges of a triangle-free graph into 4-stars (degree-three vertices) is NP-hard. This yields an alternative proof that 3-anonymity is NP-hard even when the database attributes are all binary.
-
3-anonymity with only 27 attributes per record is MAX SNP-hard.
-
For databases with n rows, k-anonymity is in O(4n ·poly(n))) time for all k > 1.
-
For databases with ℓ attributes, alphabet size c, and n rows, k-Anonymity can be solved in \(2^{O(k^2 (2c)^\ell)} + O(n \ell)\) time.
-
3-diversity with binary attributes is NP-hard, with one sensitive attribute.
-
2-diversity with binary attributes is NP-hard, with three sensitive attributes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
Agrawal, R., Srikant, R.: Privacy-preserving data mining. ACM SIGMOD Rec. 29(2), 439–450 (2000)
Anshelevich, E., Karagiozova, A.: Terminal backup, 3D matching, and covering cubic graphs. In: Proceedings of the 39th ACM Symposium on Theory of Computing, pp. 391–400 (2007)
Blocki, J., Williams, R.: Resolving the Complexity of Some Data Privacy Problems. arXiv:1004.3811 (2010)
Bonizzoni, P., Della Vedova, G., Dondi, R.: The k-anonymity problem is hard. In: Gȩbala, M. (ed.) FCT 2009. LNCS, vol. 5699, pp. 26–37. Springer, Heidelberg (2009)
Chakaravarthy, V., Pandit, V., Sabharwal, Y.: On the Complexity of the k-Anonymization Problem. arXiv:1004.4729 (2010)
Dor, D., Tarsi, M.: Graph decomposition is NPC - A complete proof of Holyer’s conjecture. In: Proceedings of the 24th ACM Symposium on Theory of Computing, pp. 252–263 (1992)
Dwork, C.: Differential privacy. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 1–12. Springer, Heidelberg (2006)
Evans, P., Chaytor, R., Wareham, T.: Fixed-parameter tractability of anonymizing data by suppressing entries. Journal of Combinatorial Optimization 18(4), 362–375 (2009)
Flum, J., Grohe, M.: Parameterized complexity theory. Springer, New York (2006)
Kann, V.: Maximum bounded 3-dimensional matching is MAX SNP-complete. Information Processing Letters 37(1), 27–35 (1991)
Machanavajjhala, A., Kifer, D., Gehrke, J., Venkitasubramaniam, M.: L-diversity: Privacy beyond k-anonymity. ACM Transactions on Knowledge Discovery from Data 1(1) (2007)
Meyerson, A., Williams, R.: On the complexity of optimal K-anonymity. In: Proceedings of the 23rd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 223–228 (2004)
Papadimitriou, C., Yannakakis, M.: Optimization, approximation, and complexity classes. In: Proceedings of the 20th ACM Symposium on Theory of Computing, pp. 229–234 (1988)
Park, H., Shim, K.: Approximate algorithms for K-anonymity. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 67–78 (2007)
Samarati, P.: Protecting respondents’ identities in microdata release. IEEE Transactions on Knowledge and Data Engineering, 1010–1027 (2001)
Sweeney, L.: k-anonymity: a model for protecting privacy. International Journal on Uncertainty, Fuzziness and Knowledge-based Systems 10(5), 557–570 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blocki, J., Williams, R. (2010). Resolving the Complexity of Some Data Privacy Problems. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds) Automata, Languages and Programming. ICALP 2010. Lecture Notes in Computer Science, vol 6199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14162-1_33
Download citation
DOI: https://doi.org/10.1007/978-3-642-14162-1_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14161-4
Online ISBN: 978-3-642-14162-1
eBook Packages: Computer ScienceComputer Science (R0)