Tight Space Lower Bound for Pseudo-Deterministic Approximate Counting

04/04/2023

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by   Ofer Grossman, et al.

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We investigate one of the most basic problems in streaming algorithms: approximating the number of elements in the stream. In 1978, Morris famously gave a randomized algorithm achieving a constant-factor approximation error for streams of length at most N in space O(loglog N). We investigate the pseudo-deterministic complexity of the problem and prove a tight Ω(log N) lower bound, thus resolving a problem of Goldwasser-Grossman-Mohanty-Woodruff.