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Tight Space Lower Bound for Pseudo-Deterministic Approximate Counting (2304.01438v3)
Published 4 Apr 2023 in cs.DS and cs.CC
Abstract: 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 $O(\log \log N)$. We investigate the pseudo-deterministic complexity of the problem and prove a tight $\Omega(\log N)$ lower bound, thus resolving a problem of Goldwasser-Grossman-Mohanty-Woodruff.