Abstract
The era of big data has brought the need of fast data stream analysis. Recently the problem of streaming submodular optimization has attracted much attention due to the importance of both submodular functions and streaming analytics. However, in real practical setting, streaming data often comes with noise which causes difficulties in analysing and optimizing submodular functions. In this paper, we study the problem of submodular maximization with cardinality constraint under a noisy streaming model, where the impact of noise is assumed to be small as inspired by the framework of differential privacy (so we also call it DP noise). For this problem, we eventually give a worst-case approximation ratio of \(\frac{1}{\left( 2+\left( 1+\frac{1}{k}\right) ^{2}\right) \left( 1+\frac{1}{k}\right) }-\delta \) in one pass. To complement the theoretical analysis, we also conduct experiments across real datasets to show our algorithm outperforms the baseline streaming methods.
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Acknowledgements
The authors are supported by Natural Science Foundation of China (No. 61772005), Outstanding Youth Innovation Team Project for Universities of Shandong Province (No. 2020KJN008), Natural Science Foundation of Fujian Province (No. 2020J01845) and Educational Research Project for Young and Middle-aged Teachers of Fujian Provincial Department of Education (No. JAT190613).
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Xiao, D., Guo, L., Liao, K., Yao, P. (2021). Streaming Submodular Maximization Under Differential Privacy Noise. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Combinatorial Optimization and Applications. COCOA 2021. Lecture Notes in Computer Science(), vol 13135. Springer, Cham. https://doi.org/10.1007/978-3-030-92681-6_34
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DOI: https://doi.org/10.1007/978-3-030-92681-6_34
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