Abstract
In this paper, we give efficient algorithms and lower bounds for solving the heavy hitters problem while preserving differential privacy in the fully distributed local model. In this model, there are n parties, each of which possesses a single element from a universe of size N. The heavy hitters problem is to find the identity of the most common element shared amongst the n parties. In the local model, there is no trusted database administrator, and so the algorithm must interact with each of the n parties separately, using a differentially private protocol. We give tight information-theoretic upper and lower bounds on the accuracy to which this problem can be solved in the local model (giving a separation between the local model and the more common centralized model of privacy), as well as computationally efficient algorithms even in the case where the data universe N may be exponentially large.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
McSherry, F., Talwar, K.: Mechanism design via differential privacy. In: Proceedings of the 48th Annual Symposium on Foundations of Computer Science (2007)
Gilbert, A., Li, Y., Porat, E., Strauss, M.: Approximate sparse recovery: optimizing time and measurements. In: Proceedings of the 42nd ACM Symposium on Theory of Computing, pp. 475–484. ACM (2010)
Dwork, C., McSherry, F., Nissim, K., Smith, A.: Calibrating Noise to Sensitivity in Private Data Analysis. In: Halevi, S., Rabin, T. (eds.) TCC 2006. LNCS, vol. 3876, pp. 265–284. Springer, Heidelberg (2006)
Dwork, C.: Differential Privacy: A Survey of Results. In: Agrawal, M., Du, D.-Z., Duan, Z., Li, A. (eds.) TAMC 2008. LNCS, vol. 4978, pp. 1–19. Springer, Heidelberg (2008)
Kasiviswanathan, S., Lee, H., Nissim, K., Raskhodnikova, S., Smith, A.: What Can We Learn Privately? In: IEEE 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008, pp. 531–540 (2008)
Beimel, A., Nissim, K., Omri, E.: Distributed Private Data Analysis: Simultaneously Solving How and What. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 451–468. Springer, Heidelberg (2008)
Gupta, A., Hardt, M., Roth, A., Ullman, J.: Privately Releasing Conjunctions and the Statistical Query Barrier. In: Proceedings of the 43rd annual ACM Symposium on the Theory of Computing. ACM, New York (2011)
McGregor, A., Mironov, I., Pitassi, T., Reingold, O., Talwar, K., Vadhan, S.: The limits of two-party differential privacy. In: Proceedings of the 51st Annual IEEE Symposium on Foundations of Computer Science (FOCS), pp. 81–90. IEEE (2010)
Dwork, C., Naor, M., Pitassi, T., Rothblum, G., Yekhanin, S.: Pan-private streaming algorithms. In: Proceedings of ICS (2010)
Mir, D., Muthukrishnan, S., Nikolov, A., Wright, R.: Pan-private algorithms via statistics on sketches. In: Proceedings of the 30th Symposium on Principles of Database Systems of Data, pp. 37–48. ACM (2011)
Blum, A., Ligett, K., Roth, A.: A learning theory approach to non-interactive database privacy. In: Proceedings of the 40th Annual ACM Symposium on Theory of Computing, pp. 609–618. ACM (2008)
Blum, A., Roth, A.: Fast private data release algorithms for sparse queries. CoRR, abs/1111.6842 (2011)
Dwork, C., McSherry, F., Talwar, K.: The price of privacy and the limits of LP decoding. In: Proceedings of the Thirty-Ninth Annual ACM Symposium on Theory of Computing, p. 94. ACM (2007)
Li, Y., Zhang, Z., Winslett, M., Yang, Y.: Compressive mechanism: Utilizing sparse representation in differential privacy. In: Proceedings of the 10th Annual ACM Workshop on Privacy in the Electronic Society, pp. 177–182. ACM (2011)
Hsu, J., Khanna, S., Roth, A.: Distributed private heavy hitters. Arxiv preprint arXiv:1202.4910 (2012)
Dinur, I., Nissim, K.: Revealing information while preserving privacy. In: 22nd ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS 2003), pp. 202–210 (2003)
Beimel, A., Kasiviswanathan, S., Nissim, K.: Bounds on the sample complexity for private learning and private data release. Theory of Cryptography, 437–454 (2010)
Hardt, M., Talwar, K.: On the Geometry of Differential Privacy. In: The 42nd ACM Symposium on the Theory of Computing, STOC 2010 (2010)
Gupta, A., Ligett, K., McSherry, F., Roth, A., Talwar, K.: Differentially Private Combinatorial Optimization. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hsu, J., Khanna, S., Roth, A. (2012). Distributed Private Heavy Hitters. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_39
Download citation
DOI: https://doi.org/10.1007/978-3-642-31594-7_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31593-0
Online ISBN: 978-3-642-31594-7
eBook Packages: Computer ScienceComputer Science (R0)