Tight Data Access Bounds for Private Top-k Selection
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We study the top-k selection problem under the differential privacy model: m items are rated according to votes of a set of clients. We consider a setting in which algorithms can retrieve data via a sequence of accesses, each either a random access or a sorted access; the goal is to minimize the total number of data accesses. Our algorithm requires only O(√(mk)) expected accesses: to our knowledge, this is the first sublinear data-access upper bound for this problem. Our analysis also shows that the well-known exponential mechanism requires only O(√(m)) expected accesses. Accompanying this, we develop the first lower bounds for the problem, in three settings: only random accesses; only sorted accesses; a sequence of accesses of either kind. We show that, to avoid Ω(m) access cost, supporting *both* kinds of access is necessary, and that in this case our algorithm's access cost is optimal.
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