The complexity of massive data set computations

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The structure of optimal private tests for simple hypotheses (2018, methodology): “ based on these randomized samples. Our characterization in the general case is more involved, as it exhibits several distinct regimes for the parameter ε. 1This statement is folklore, but see, e.g., [BY02] for the lower bound, [Can17] or Corollary 2.2 for the upper bound. 2 Our analysis relies on a”
Strong Lower Bounds for Approximating Distribution Support Size and the Distinct Elements Problem (2007, unknown): “Bar-Yossef proved that for all functions invariant under permutations, algorithms that take O( √ n) uniform samples without replacement can be simulated by algorithms that take the same number of samples with replacement.”
Numerical linear algebra in the streaming model (2009, background): “Indeed, for estimating the Euclidean norm of a length-n data stream, the sampling complexity is Ω( √ n) [4], while there is a sketching algorithm achieving O((logn)/ε(2)) bits of space [3].”
Clustering Large Graphs via the Singular Value Decomposition (2004, background): “More recently, Bar-Yossef (2002, 2003) addressed the question of the optimality of our algorithms.”