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:
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2-anonymity is in P.
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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.
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3-anonymity with only 27 attributes per record is MAX SNP-hard.
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For databases with n rows, k-anonymity is in O(4n ·poly(n))) time for all k > 1.
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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.
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3-diversity with binary attributes is NP-hard, with one sensitive attribute.
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2-diversity with binary attributes is NP-hard, with three sensitive attributes.
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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)
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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
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DOI: https://doi.org/10.1007/978-3-642-14162-1_33
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