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Chapter and Conference Paper
Nearly Optimal Private Convolution
We study algorithms for computing the convolution of a private input x with a public input h, while satisfying the guarantees of (ε, δ)-differential privacy. Convolution is a fundamental operation, intimately rel...
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Chapter
Frugal Streaming for Estimating Quantiles
Modern applications require processing streams of data for estimating statistical quantities such as quantiles with small amount of memory. In many such applications, in fact, one needs to compute such statist...
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Chapter and Conference Paper
Range Medians
We study a generalization of the classical median finding problem to batched query case: given an array of unsorted n items and k (not necessarily disjoint) intervals in the array, the goal is to determine the me...
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Chapter and Conference Paper
Radix Sorting with No Extra Space
It is well known that n integers in the range [1,n c ] can be sorted in O(n) time in the RAM model using radix sorting. More generally, integers in any range [1,
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Chapter and Conference Paper
Subspace Sampling and Relative-Error Matrix Approximation: Column-Row-Based Methods
Much recent work in the theoretical computer science, linear algebra, and machine learning has considered matrix decompositions of the following form: given an m ×n matrix A, decompose it as a product of three ma...
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Chapter and Conference Paper
Workload-Optimal Histograms on Streams
A histogram is a piecewise-constant approximation of an observed data distribution. A histogram is used as a small-space, approximate synopsis of the underlying data distribution, which is often too large to b...