# Differentially Private K-Skyband Query Answering Through Adaptive Spatial Decomposition

## Abstract

Given a set of multi-dimensional points, a \(k\)-skyband query retrieves those points dominated by no more than *k* other points. \(k\)-skyband queries are an important type of multi-criteria analysis with diverse applications in practice. In this paper, we investigate techniques to answer \(k\)-skyband queries with differential privacy. We first propose a general technique BBS-Priv, which accepts any differentially private spatial decomposition tree as input and leverages data synthesis to answer \(k\)-skyband queries privately. We then show that, though quite a few private spatial decomposition trees are proposed in the literature, they are mainly designed to answer spatial range queries. Directly integrating them with BBS-Priv would introduce too much noise to generate useful \(k\)-skyband results. To address this problem, we propose a novel spatial decomposition technique k-skyband tree specially optimized for *k*-skyband queries, which partitions data adaptively based on the parameter *k*. We further propose techniques to generate a k-skyband tree over spatial data that satisfies differential privacy, and combine BBS-Priv with the private k-skyband tree to answer \(k\)-skyband queries. We conduct extensive experiments based on two real-world datasets and three synthetic datasets that are commonly used for evaluating \(k\)-skyband queries. The results show that the proposed scheme significantly outperforms existing differentially private spatial decomposition schemes and achieves high utility when privacy budgets are properly allocated.

## Keywords

*k*-skyband query Differential privacy Adaptive spatial decomposition

## Supplementary material

## References

- 1.
- 2.Nba players statistics. http://www.hoopsstats.com/basketball/fantasy/nba/playerstats
- 3.Barak, B., Chaudhuri, K., Dwork, C., Kale, S., McSherry, F., Talwar, K.: Privacy, accuracy, and consistency too: a holistic solution to contingency table release (2007)Google Scholar
- 4.Blanton, M., Aguiar, E.: Private and oblivious set and multiset operations. In: ASIACCS (2012)Google Scholar
- 5.Borzsony, S., Kossmann, D., Stocker, K.: The skyline operator. In: ICDE (2001)Google Scholar
- 6.Cachin, C.: Efficient private bidding and auctions with an oblivious third party. In: CCS (1999)Google Scholar
- 7.Chen, L., Gao, S., Anyanwu, K.: Efficiently evaluating skyline queries on RDF databases. In: ESWC (2011)Google Scholar
- 8.Chen, L., Yu, T., Chirkova, R.: Wavecluster with differential privacy. In: CIKM (2015)Google Scholar
- 9.Cormode, G., Procopiuc, C., Srivastava, D., Shen, E., Yu, T.: Differentially private spatial decompositions. In: ICDE (2012)Google Scholar
- 10.Dwork, C.: Differential privacy: a survey of results. In: TAMC (2008)Google Scholar
- 11.Dwork, C., Lei, J.: Differential privacy and robust statistics. In: STOC (2009)Google Scholar
- 12.Dwork, C., McSherry, F., Nissim, K., Smith, A.: Calibrating noise to sensitivity in private data analysis. In: TCC (2006)Google Scholar
- 13.Dwork, C., Roth, A.: The algorithmic foundations of differential privacy. Found. Trends Theor. Comput. Sci.
**9**, 211–407 (2014)MathSciNetCrossRefzbMATHGoogle Scholar - 14.Feldman, D., Fiat, A., Kaplan, H., Nissim, K.: Private coresets. In: STOC (2009)Google Scholar
- 15.Feng, X., Gao, Y., Jiang, T., Chen, L., Miao, X., Liu, Q.: Parallel k-skyband computation on multicore architecture. In: APWeb (2013)Google Scholar
- 16.Ghinita, G., Zhao, K., Papadias, D., Kalnis, P.: A reciprocal framework for spatial k-anonymity. Inf. Syst.
**35**(3), 299–314 (2010)CrossRefGoogle Scholar - 17.Gordon, D.S., Carmit, H., Katz, J., Lindell, Y.: Complete fairness in secure two-party computation. In: STOC (2008)Google Scholar
- 18.Harnik, D., Naor, M., Reingold, O., Rosen, A.: Completeness in two-party secure computation: a computational view. In: STOC (2004)Google Scholar
- 19.Hay, M., Rastogi, V., Miklau, G., Suciu, D.: Boosting the accuracy of differentially private histograms through consistency. PVLDB
**3**, 1021–1032 (2010)Google Scholar - 20.Inan, A., Kantarcioglu, M., Ghinita, G., Bertino, E.: Private record matching using differential privacy. In: EDBT (2010)Google Scholar
- 21.Kasiviswanathan, S.P., Lee, H.K., Nissim, K., Raskhodnikova, S., Smith, A.: What can we learn privately? In: FOCS (2008)Google Scholar
- 22.Kodama, K., Iijima, Y., Guo, X., Ishikawa, Y.: Skyline queries based on user locations and preferences for making location-based recommendations. In: International Workshop on Location Based Social Networks (2009)Google Scholar
- 23.Levandoski, J.J., Mokbel, M.F., Khalefa, M.E.: Preference query evaluation over expensive attributes. In: CIKM (2010)Google Scholar
- 24.Machanavajjhala, A., Kifer, D., Gehrke, J., Venkitasubramaniam, M.: L-diversity: privacy beyond k-anonymity. ACM Trans. Knowl. Discov. Data
**1**(1) (2007). http://doi.acm.org/10.1145/1217299.1217302 - 25.Magnani, M., Assent, I., Mortensen, M.L.: Taking the big picture: representative skylines based on significance and diversity. VLDB J.
**23**(5), 795–815 (2014)CrossRefGoogle Scholar - 26.McSherry, F., Talwar, K.: Mechanism design via differential privacy. In: FOCS (2007)Google Scholar
- 27.McSherry, F.: Privacy integrated queries: an extensible platform for privacy-preserving data analysis. Commun. ACM
**53**(9), 19–30 (2010)CrossRefGoogle Scholar - 28.Freedman, M.J., Nissim, K., Pinkas, B.: Efficient private matching and set intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004). doi: 10.1007/978-3-540-24676-3_1 CrossRefGoogle Scholar
- 29.Nissim, K., Raskhodnikova, S., Smith, A.: Smooth sensitivity and sampling in private data analysis. In: STOC (2007)Google Scholar
- 30.Papadias, D., Tao, Y., Fu, G., Seeger, B.: Progressive skyline computation in database systems. ACM Trans. Database Syst.
**30**(1), 41–82 (2005)CrossRefGoogle Scholar - 31.Samarati, P., Sweeney, L.: Protecting privacy when disclosing information: k-anonymity and its enforcement through generalization and suppression. In: Proceedings IEEE Security & Privacy (1998)Google Scholar
- 32.Sheikholeslami, G., Chatterjee, S., Zhang, A.: Wavecluster: a multi-resolution clustering approach for very large spatial databases. In: VLDB (1998)Google Scholar
- 33.Sheikholeslami, G., Chatterjee, S., Zhang, A.: Wavecluster: a wavelet-based clustering approach for spatial data in very large databases. VLDB J.
**8**(3–4), 289–304 (2000)CrossRefGoogle Scholar - 34.Vaidya, J., Clifton, C.: Privacy-preserving top-k queries. In: ICDE (2005)Google Scholar
- 35.Valkanas, G., Papadopoulos, A.N., Gunopulos, D.: Skydiver: a framework for skyline diversification. In: EDBT (2013)Google Scholar
- 36.Xu, J., Zhang, Z., Xiao, X., Yang, Y., Yu, G., Winslett, M.: Differentially private histogram publication. VLDB J.
**22**(6), 797–822 (2013)CrossRefGoogle Scholar - 37.Zhang, J., Xiao, X., Xie, X.: Privtree: a differentially private algorithm for hierarchical decompositions. In: SIGMOD (2016)Google Scholar
- 38.Zhang, J., Xiao, X., Yang, Y., Zhang, Z., Winslett, M.: Privgene: differentially private model fitting using genetic algorithms. In: SIGMOD (2013)Google Scholar